第2章方程式と不等式Equations and Inequalities

Answer Key解答

Solution 1解答 1

$x$	$y = \frac{1}{2} x + 2$	$(x, y)$
$−2$	$y = \frac{1}{2} (−2) + 2 = 1$	$(−2, 1)$
$−1$	$y = \frac{1}{2} (−1) + 2 = \frac{3}{2}$	$(- 1, \frac{3}{2})$
$0$	$y = \frac{1}{2} (0) + 2 = 2$	$(0, 2)$
$1$	$y = \frac{1}{2} (1) + 2 = \frac{5}{2}$	$(1, \frac{5}{2})$
$2$	$y = \frac{1}{2} (2) + 2 = 3$	$(2, 3)$

This is an image of a graph on an x, y coordinate plane. The x and y-axis range from negative 5 to 5. A line passes through the points (-2, 1); (-1, 3/2); (0, 2); (1, 5/2); and (2, 3).

Solution 2解答 2

x-intercept is $(4, 0);$ y-intercept is $(0, 3) .$

x切片は $(4, 0);$ 、y切片は $(0, 3)$

This is an image of a line graph on an x, y coordinate plane. The x and y axes range from negative 4 to 6. The function y = -3x/4 + 3 is plotted.

Solution 3解答 3

$\sqrt{125} = 5 \sqrt{5}$

Solution 4解答 4

$(- 5, \frac{5}{2})$

Solution 1解答 1

$x = −5$

Solution 2解答 2

$x = −3$

Solution 3解答 3

$x = \frac{10}{3}$

Solution 4解答 4

$x = 1$

Solution 5解答 5

$x = - \frac{7}{17} .$ Excluded values are $x = - \frac{1}{2}$ and $x = - \frac{1}{3} .$

$x = - \frac{7}{17}$ 除外される値は $x = - \frac{1}{2}$ と $x = - \frac{1}{3}$

Solution 6解答 6

$x = \frac{1}{3}$

Solution 7解答 7

$m = - \frac{2}{3}$

Solution 8解答 8

$y = 4 x −3$

Solution 9解答 9

$x + 3 y = 2$

Solution 10解答 10

Horizontal line: $y = 2$

横の直線: $y = 2$

Solution 11解答 11

Parallel lines: equations are written in slope-intercept form.

平行な直線。方程式は傾き切片形で書いてある。

Coordinate plane with the x-axis ranging from negative 5 to 5 and the y-axis ranging from negative 1 to 6. Two functions are graphed on the same plot: y = x/2 plus 5 and y = x/2 plus 2. The lines do not cross.

Solution 12解答 12

$y = 5 x + 3$

Solution 1解答 1

11 and 25

11と25

Solution 2解答 2

$C = 2.5 x + 3, 650$

Solution 3解答 3

45 mi/h

時速45マイル

Solution 4解答 4

$L = 37$ cm, $W = 18$ cm

$L = 37$ cm、 $W = 18$ cm

Solution 5解答 5

250 ft²

250平方フィート

Solution 1解答 1

$\sqrt{−24} = 0 + 2 i \sqrt{6}$

Solution 2解答 2

Coordinate plane with the x and y axes ranging from negative 5 to 5. The point -4 i is plotted.

Solution 3解答 3

$(3 −4 i) - (2 + 5 i) = 1 −9 i$

Solution 4解答 4

$\frac{5}{2} - i$

Solution 5解答 5

$18 + i$

Solution 6解答 6

$−3 −4 i$

Solution 7解答 7

$−1$

Solution 1解答 1

$(x - 6) (x + 1) = 0; x = 6, x = - 1$

Solution 2解答 2

$(x −7) (x + 3) = 0,$ $x = 7,$ $x = −3.$

Solution 3解答 3

$(x + 5) (x −5) = 0,$ $x = −5,$ $x = 5.$

Solution 4解答 4

$(3 x + 2) (4 x + 1) = 0,$ $x = - \frac{2}{3},$ $x = - \frac{1}{4}$

Solution 5解答 5

$x = 0, x = −10, x = −1$

Solution 6解答 6

$x = 4 \pm \sqrt{5}$

Solution 7解答 7

$x = 3 \pm \sqrt{22}$

Solution 8解答 8

$x = - \frac{2}{3},$ $x = \frac{1}{3}$

Solution 9解答 9

$5$ units

$5$ 単位

Solution 1解答 1

$\frac{1}{4}$

Solution 2解答 2

$25$

Solution 3解答 3

${−1}$

Solution 4解答 4

$0,$ $\frac{1}{2},$ $- \frac{1}{2}$

Solution 5解答 5

$1;$ extraneous solution $- \frac{2}{9}$

$1;$ 外来解は $- \frac{2}{9}$

Solution 6解答 6

$−2;$ extraneous solution $−1$

$−2;$ 外来解は $−1$

Solution 7解答 7

$−1,$ $\frac{3}{2}$

Solution 8解答 8

$−3, 3, - i, i$

Solution 9解答 9

$2, 12$

Solution 10解答 10

$−1$ ( $0$ is not a solution).

$−1$ ( $0$ は解ではない)。

Solution 1解答 1

$[−3, 5]$

Solution 2解答 2

$(- \infty, −2) \cup [3, \infty)$

Solution 3解答 3

$x < 1$

Solution 4解答 4

$x \geq −5$

Solution 5解答 5

$(2, \infty)$

Solution 6解答 6

$[- \frac{3}{14}, \infty)$

Solution 7解答 7

$6 < x \leq 9 or (6, 9]$

式中の英語：or：または

Solution 8解答 8

$(- \frac{1}{8}, \frac{1}{2})$

Solution 9解答 9

$| x −2 | \leq 3$

Solution 10解答 10

$k \leq 1$ or $k \geq 7;$ in interval notation, this would be $(- \infty, 1] \cup [7, \infty) .$

$k \leq 1$ または $k \geq 7;$ 。区間の書き方では $(- \infty, 1] \cup [7, \infty)$ となる。

A coordinate plane with the x-axis ranging from -1 to 9 and the y-axis ranging from -3 to 8. The function y = -2|k 4| + 6 is graphed and everything above the function is shaded in.

2.1 Section Exercises2.1 節末問題

Solution 1解答 1

Answers may vary. Yes. It is possible for a point to be on the x-axis or on the y-axis and therefore is considered to NOT be in one of the quadrants.

答えは一通りとは限らない。ありうる。点が x軸上や y軸上にあることはあり、その場合はどの象限にも入らないとみなされる。

Solution 3解答 3

The y-intercept is the point where the graph crosses the y-axis.

y切片とは、グラフが y軸と交わる点である。

Solution 5解答 5

The x-intercept is $(2, 0)$ and the y-intercept is $(0, 6) .$

x切片は $(2, 0)$ 、y切片は $(0, 6)$ である。

Solution 7解答 7

The x-intercept is $(2, 0)$ and the y-intercept is $(0, −3) .$

x切片は $(2, 0)$ 、y切片は $(0, −3)$ である。

Solution 9解答 9

The x-intercept is $(3, 0)$ and the y-intercept is $(0, \frac{9}{8}) .$

x切片は $(3, 0)$ 、y切片は $(0, \frac{9}{8})$ である。

Solution 11解答 11

$y = 4 - 2 x$

Solution 13解答 13

$y = \frac{5 - 2 x}{3}$

Solution 15解答 15

$y = 2 x - \frac{4}{5}$

Solution 17解答 17

$d = \sqrt{74}$

Solution 19解答 19

$d = \sqrt{36} = 6$

Solution 21解答 21

$d \approx 62.97$

Solution 23解答 23

$(3, \frac{- 3}{2})$

Solution 25解答 25

$(2, −1)$

Solution 27解答 27

$(0, 0)$

Solution 29解答 29

$y = 0$

Solution 31解答 31

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 5 to 5. The points (0,4); (-1,2) and (2,1) are plotted and labeled.

not collinear

同一直線上にない

Solution 33解答 33

$A: (−3, 2), B: (1, 3), C: (4, 0)$

Solution 35解答 35

$x$	$y$
$−3$	1
0	2
3	3
6	4

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10. The points (-3, 1); (0, 2); (3, 3) and (6, 4) are plotted and labeled. A line runs through all these points.

Solution 37解答 37

x	y
–3	0
0	1.5
3	3

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10. The points (-3, 0); (0, 1.5) and (3, 3) are plotted and labeled. A line runs through all of these points.

Solution 39解答 39

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10. The points (8, 0) and (0, -4) are plotted and labeled. A line runs through both of these points.

Solution 41解答 41

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10. The points (0, 2) and (3, 0) are plotted and labeled. A line runs through both of these points.

Solution 43解答 43

$d = 8.246$

Solution 45解答 45

$d = 5$

Solution 47解答 47

$(−3, 4)$

Solution 49解答 49

$x = 0 y = −2$

Solution 51解答 51

$x = 0.75 y = 0$

Solution 53解答 53

$x = - 1.667 y = 0$

Solution 55解答 55

$15 - 11.2 = 3.8 mi$ shorter

$15 - 11.2 = 3.8 mi$ だけ短い

Solution 57解答 57

$6 .0 42$

Solution 59解答 59

Midpoint of each diagonal is the same point $(2, 2)$ . Note this is a characteristic of rectangles, but not other quadrilaterals.

どちらの対角線の中点も同じ点 $(2, 2)$ である。これは長方形の特徴であり、ほかの四角形では成り立たないことに注意せよ。

Solution 61解答 61

37mi

37マイル

Solution 63解答 63

54 ft

54フィート

2.2 Section Exercises2.2 節末問題

Solution 1解答 1

It means they have the same slope.

傾きが同じだということである。

Solution 3解答 3

The exponent of the $x$ variable is 1. It is called a first-degree equation.

$x$ の変数の指数が1である。これを一次方程式という。

Solution 5解答 5

If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

どちらの値を方程式に入れても、方程式の中の式が定義されなくなる(分母が0になる)。

Solution 7解答 7

$x = 2$

Solution 9解答 9

$x = \frac{2}{7}$

Solution 11解答 11

$x = 6$

Solution 13解答 13

$x = 3$

Solution 15解答 15

$x = −14$

Solution 17解答 17

$x \neq −4;$ $x = −3$

Solution 19解答 19

$x \neq 1;$ when we solve this we get $x = 1,$ which is excluded, therefore NO solution

$x \neq 1;$ これを解くと $x = 1$ になるが、これは除外される値なので、解は無い。

Solution 21解答 21

$x \neq 0;$ $x = - \frac{5}{2}$

Solution 23解答 23

$y = - \frac{4}{5} x + \frac{14}{5}$

Solution 25解答 25

$y = - \frac{3}{4} x + 2$

Solution 27解答 27

$y = \frac{1}{2} x + \frac{5}{2}$

Solution 29解答 29

$y = −3 x - 5$

Solution 31解答 31

$y = 7$

Solution 33解答 33

$y = −4$

Solution 35解答 35

$8 x + 5 y = 7$

Solution 37解答 37

Coordinate plane with the x and y axes ranging from negative 10 to 10. The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot. The lines do not cross.

Parallel

平行

Solution 39解答 39

Coordinate plane with the x and y axes ranging from negative 10 to 10. The function y = negative 3 and the line x = 4 are graphed on the same plot. These lines cross at a 90 degree angle.

Perpendicular

垂直

Solution 41解答 41

$m = - \frac{9}{7}$

Solution 43解答 43

$m = \frac{3}{2}$

Solution 45解答 45

$m_{1} = - \frac{1}{3}, m_{2} = 3; Perpendicular .$

Solution 47解答 47

$y = 0.245 x - 45.662.$ Answers may vary. $y_{min} = −50, y_{max} = −40$

$y = 0.245 x - 45.662.$ 答えは一通りとは限らない。 $y_{min} = −50, y_{max} = −40$

Solution 49解答 49

$y = - 2.333 x + 6.667.$ Answers may vary. $y_{\min} = −10, y_{\max} = 10$

$y = - 2.333 x + 6.667.$ 答えは一通りとは限らない。 $y_{\min} = −10, y_{\max} = 10$

Solution 51解答 51

$y = - \frac{A}{B} x + \frac{C}{B}$

Solution 53解答 53

$\begin{array}{l} The slope for (−1, 1) to (0, 4) is 3. \\ The slope for (−1, 1) to (2, 0) is \frac{- 1}{3} . \\ The slope for (2, 0) to (3, 3) is 3. \\ The slope for (0, 4) to (3, 3) is \frac{- 1}{3} . \end{array}$

Yes they are perpendicular.

垂直である。

Solution 55解答 55

30 ft

30フィート

Solution 57解答 57

$57.50

Solution 59解答 59

220 mi

220マイル

2.3 Section Exercises2.3 節末問題

Solution 1解答 1

Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.

答えは一通りとは限らない。ありうる答え: 変数が何を表すかを言葉で定めるべきである。変数を宣言するべきである。見出しを付けるべきである。

Solution 3解答 3

$2, 000 - x$

Solution 5解答 5

$v + 10$

Solution 7解答 7

Ann: $23;$ Beth: $46$

Solution 9解答 9

$20 + 0.05 m$

Solution 11解答 11

300 min

300分

Solution 13解答 13

$90 + 40 P$

Solution 15解答 15

6 devices

6台

Solution 17解答 17

$50, 000 - x$

Solution 19解答 19

4 h

Solution 21解答 21

She traveled for 2 h at 20 mi/h, or 40 miles.

時速20マイルで2時間、すなわち40マイル走った。

Solution 23解答 23

$5,000 at 8% and $15,000 at 12%

8%に5,000ドル、12%に15,000ドル

Solution 25解答 25

$B = 100 + .05 x$

Solution 27解答 27

Plan A

契約A

Solution 29解答 29

$R = 9$

Solution 31解答 31

$r = \frac{4}{5}$ or 0.8

$r = \frac{4}{5}$ すなわち0.8

Solution 33解答 33

$W = \frac{P - 2 L}{2} = \frac{58 - 2 (15)}{2} = 14$

Solution 35解答 35

$f = \frac{p q}{p + q} = \frac{8 (13)}{8 + 13} = \frac{104}{21}$

Solution 37解答 37

$m = \frac{- 5}{4}$

Solution 39解答 39

$h = \frac{2 A}{b_{1} + b_{2}}$

Solution 41解答 41

length = 360 ft; width = 160 ft

縦 = 360フィート、横 = 160フィート

Solution 43解答 43

405 mi

405マイル

Solution 45解答 45

$A = 88 in .^{2}$

Solution 47解答 47

28.7

Solution 49解答 49

$h = \frac{V}{π r^{2}}$

Solution 51解答 51

$r = \sqrt{\frac{V}{π h}}$

Solution 53解答 53

$C = 12 π$

2.4 Section Exercises2.4 節末問題

Solution 1解答 1

Add the real parts together and the imaginary parts together.

実部どうしを足し、虚部どうしを足す。

Solution 3解答 3

Possible answer: $i$ times $i$ equals -1, which is not imaginary.

ありうる答え: $i$ に $i$ を掛けると −1 になり、これは虚数ではない。

Solution 5解答 5

$−8 + 2 i$

Solution 7解答 7

$14 + 7 i$

Solution 9解答 9

$- \frac{23}{29} + \frac{15}{29} i$

Solution 11解答 11

Coordinate plane with the x and y axes ranging from 5 to 5. The point 1 2i is plotted

Solution 13解答 13

Coordinate plane with the x and y axes ranging from -5 to 5. The point i is plotted.

Solution 15解答 15

$8 - i$

Solution 17解答 17

$−11 + 4 i$

Solution 19解答 19

$2 −5 i$

Solution 21解答 21

$6 + 15 i$

Solution 23解答 23

$−16 + 32 i$

Solution 25解答 25

$−4 −7 i$

Solution 27解答 27

Solution 29解答 29

$2 - \frac{2}{3} i$

Solution 31解答 31

$4 - 6 i$

Solution 33解答 33

$\frac{2}{5} + \frac{11}{5} i$

Solution 35解答 35

$15 i$

Solution 37解答 37

$1 + i \sqrt{3}$

Solution 39解答 39

$1$

Solution 41解答 41

$−1$

Solution 43解答 43

128i

Solution 45解答 45

${(\frac{\sqrt{3}}{2} + \frac{1}{2} i)}^{6} = −1$

Solution 47解答 47

$3 i$

Solution 49解答 49

Solution 51解答 51

$5 −5 i$

Solution 53解答 53

$−2 i$

Solution 55解答 55

$\frac{9}{2} - \frac{9}{2} i$

2.5 Section Exercises2.5 節末問題

Solution 1解答 1

It is a second-degree equation (the highest variable exponent is 2).

二次の方程式である(変数の最も高い指数が2)。

Solution 3解答 3

We want to take advantage of the zero property of multiplication in the fact that if $a \cdot b = 0$ then it must follow that each factor separately offers a solution to the product being zero: $a = 0 o r b = 0.$

乗法の零因子の性質を使いたいからである。 $a \cdot b = 0$ なら、積が0になるにはそれぞれの因数が別々に解を与えなければならない。 $a = 0 o r b = 0.$

Solution 5解答 5

One, when no linear term is present (no x term), such as $x^{2} = 16.$ Two, when the equation is already in the form ${(a x + b)}^{2} = d .$

一つは、 $x^{2} = 16.$ のように一次の項(x の項)が無いとき。もう一つは、方程式がすでに ${(a x + b)}^{2} = d$ の形になっているとき。

Solution 7解答 7

$x = 6,$ $x = 3$

Solution 9解答 9

$x = \frac{- 5}{2},$ $x = \frac{- 1}{3}$

Solution 11解答 11

$x = 5,$ $x = −5$

Solution 13解答 13

$x = \frac{- 3}{2},$ $x = \frac{3}{2}$

Solution 15解答 15

$x = −2, 3$

Solution 17解答 17

$x = 0,$ $x = \frac{- 3}{7}$

Solution 19解答 19

$x = −6,$ $x = 6$

Solution 21解答 21

$x = 6,$ $x = −4$

Solution 23解答 23

$x = 1,$ $x = −2$

Solution 25解答 25

$x = −2,$ $x = 11$

Solution 27解答 27

$x = 3 \pm \sqrt{22}$

Solution 29解答 29

$z = \frac{2}{3},$ $z = - \frac{1}{2}$

Solution 31解答 31

$x = \frac{3 \pm \sqrt{17}}{4}$

Solution 33解答 33

Not real

実数でない

Solution 35解答 35

One rational

有理数の解が一つ

Solution 37解答 37

Two real; rational

実数の解が二つ。有理数

Solution 39解答 39

$x = \frac{- 1 \pm \sqrt{17}}{2}$

Solution 41解答 41

$x = \frac{5 \pm \sqrt{13}}{6}$

Solution 43解答 43

$x = \frac{- 1 \pm \sqrt{17}}{8}$

Solution 45解答 45

$x \approx 0.131$ and $x \approx 2.535$

$x \approx 0.131$ と $x \approx 2.535$

Solution 47解答 47

$x \approx - 6.7$ and $x \approx 1.7$

$x \approx - 6.7$ と $x \approx 1.7$

Solution 49解答 49

$\begin{matrix} a x^{2} + b x + c & = & 0 \\ x^{2} + \frac{b}{a} x & = & \frac{- c}{a} \\ x^{2} + \frac{b}{a} x + \frac{b^{2}}{4 a^{2}} & = & \frac{- c}{a} + \frac{b}{4 a^{2}} \\ {(x + \frac{b}{2 a})}^{2} & = & \frac{b^{2} - 4 a c}{4 a^{2}} \\ x + \frac{b}{2 a} & = & \pm \sqrt{\frac{b^{2} - 4 a c}{4 a^{2}}} \\ x & = & \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} \end{matrix}$

Solution 51解答 51

$x (x + 10) = 119;$ 7 ft. and 17 ft.

$x (x + 10) = 119;$ 7フィートと17フィート

Solution 53解答 53

maximum at $x = 70$

$x = 70$ で最大

Solution 55解答 55

The quadratic equation would be $(100 x −0.5 x^{2}) - (60 x + 300) = 300.$ The two values of $x$ are 20 and 60.

二次方程式は $(100 x −0.5 x^{2}) - (60 x + 300) = 300.$ となる。 $x$ の二つの値は20と60である。

Solution 57解答 57

3 feet

3フィート

2.6 Section Exercises2.6 節末問題

Solution 1解答 1

This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.

これは無理方程式の解ではない。両辺を二乗したことで方程式の符号が変わってしまい、その結果もとの方程式では解にならなかった値である。

Solution 3解答 3

They are probably trying to enter negative 9, but taking the square root of $−9$ is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in $−27.$

おそらく −9 を入れようとしているのだろうが、 $−9$ の平方根は実数ではない。負の符号はその前に付いているので、友人は9の平方根をとり、それを三乗し、そのうえで負の符号を前に付けるべきである。結果は $−27.$ になる。

Solution 5解答 5

A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.

有理数の指数は分数である。分母が何乗根をとるか(根号の指数)を、分子が何乗するかを表す。

Solution 7解答 7

$x = 81$

Solution 9解答 9

$x = 17$

Solution 11解答 11

$x = 8, x = 27$

Solution 13解答 13

$x = −2, 1, −1$

Solution 15解答 15

$y = 0, \frac{3}{2}, \frac{- 3}{2}$

Solution 17解答 17

$m = 1, −1$

Solution 19解答 19

$x = \frac{2}{5}, ±3 i$

Solution 21解答 21

$x = 32$

Solution 23解答 23

$t = \frac{44}{3}$

Solution 25解答 25

$x = 3$

Solution 27解答 27

$x = −2$

Solution 29解答 29

$x = 4, \frac{−4}{3}$

Solution 31解答 31

$x = \frac{- 5}{4}, \frac{7}{4}$

Solution 33解答 33

$x = 3, −2$

Solution 35解答 35

$x = −5$

Solution 37解答 37

$x = 1, −1, 3, -3$

Solution 39解答 39

$x = 2, −2$

Solution 41解答 41

$x = 1, 5$

Solution 43解答 43

$x \geq 0$

Solution 45解答 45

$x = 4, 6, −6, −8$

Solution 47解答 47

10 in.

10インチ

Solution 49解答 49

90 kg

2.7 Section Exercises2.7 節末問題

Solution 1解答 1

When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

両辺を負の数で割ると両辺の符号が変わるので、不等号の向きも変わる。

Solution 3解答 3

$(- \infty, \infty)$

Solution 5解答 5

We start by finding the x-intercept, or where the function = 0. Once we have that point, which is $(3, 0),$ we graph to the right the straight line graph $y = x −3,$ and then when we draw it to the left we plot positive y values, taking the absolute value of them.

まず x切片、すなわち関数が0になるところを求める。その点 $(3, 0)$ が求まったら、そこから右へ直線 $y = x −3$ のグラフを描く。そして左へ描くときは、y の値の絶対値をとって正の値として打つ。

Solution 7解答 7

$(- \infty, \frac{3}{4}]$

Solution 9解答 9

$[- \frac{13}{2}, \infty)$

Solution 11解答 11

$(- \infty, 3)$

Solution 13解答 13

$(- \infty, - \frac{37}{3}]$

Solution 15解答 15

All real numbers $(- \infty, \infty)$

実数すべて $(- \infty, \infty)$

Solution 17解答 17

$(- \infty, - \frac{10}{3}) \cup (4, \infty)$

Solution 19解答 19

$(- \infty, −4] \cup [8, + \infty)$

Solution 21解答 21

No solution

解なし

Solution 23解答 23

$(−5, 11)$

Solution 25解答 25

$[6, 12]$

Solution 27解答 27

$[−10, 12]$

Solution 29解答 29

$\begin{array}{l} x > - 6 and x > - 2 & Take the intersection of two sets . \\ x > - 2, (- 2, + \infty) \end{array}$

式中の英語：and：および

Solution 31解答 31

$\begin{array}{l} x < - 3 or x \geq 1 & Take the union of the two sets . \\ (- \infty, - 3) {\cup^{}}^{} [1, \infty) \end{array}$

Solution 33解答 33

$(- \infty, −1) \cup (3, \infty)$

A coordinate plane where the x and y axes both range from -10 to 10. The function |x 1| is graphed and labeled along with the line y = 2. Along the x-axis there is an open circle at the point -1 with an arrow extending leftward from it. Also along the x-axis is an open circle at the point 3 with an arrow extending rightward from it.

Solution 35解答 35

$[−11, −3]$

A coordinate plane with the x-axis ranging from -14 to 10 and the y-axis ranging from -1 to 10. The function y = |x + 7| and the line y = 4 are graphed. On the x-axis theres a dot on the points -11 and -3 with a line connecting them.

Solution 37解答 37

It is never less than zero. No solution.

0より小さくなることはない。解なし。

A coordinate plane with the x and y axes ranging from -10 to 10. The function y = |x -2| and the line y = 0 are graphed.

Solution 39解答 39

Where the blue line is above the orange line; point of intersection is $x = - 3.$

青い線が橙の線より上にあるところ。交点は $x = - 3.$

$(- \infty, −3)$

A coordinate plane with the x and y axes ranging from -10 to 10. The lines y = x - 2 and y = 2x + 1 are graphed on the same axes.

Solution 41解答 41

Where the blue line is above the orange line; always. All real numbers.

青い線が橙の線より上にあるところ。つねに成り立つ。実数すべて。

$(- \infty, - \infty)$

A coordinate plane with the x and y axes ranging from -10 to 10. The lines y = x/2 +1 and y = x/2 5 are both graphed on the same axes.

Solution 43解答 43

$(−1, 3)$

Solution 45解答 45

$(- \infty, 4)$

Solution 47解答 47

${x | x < 6}$

Solution 49解答 49

${x | −3 \leq x < 5}$

Solution 51解答 51

$(−2, 1]$

Solution 53解答 53

$(- \infty, 4]$

Solution 55解答 55

Where the blue is below the orange; always. All real numbers. $(- \infty, + \infty) .$

青が橙より下にあるところ。つねに成り立つ。実数すべて。 $(- \infty, + \infty)$

A coordinate plane with the x and y axes ranging from -10 to 10. The function y = -0.5|x + 2| and the line y = 4 are graphed on the same axes. A line runs along the entire x-axis.

Solution 57解答 57

Where the blue is below the orange; $(1, 7) .$

青が橙より下にあるところ。 $(1, 7)$

A coordinate plane with the x and y axes ranging from -10 to 10. The function y = |x 4| and the line y = 3 are graphed on the same axes. Along the x-axis the points 1 and 7 have an open circle around them and a line connects the two.

Solution 59解答 59

$x = 2, \frac{- 4}{5}$

Solution 61解答 61

$(−7, 5]$

Solution 63解答 63

$\begin{array}{l} 80 \leq T \leq 120 \\ 1, 600 \leq 20 T \leq 2, 400 \end{array}$

$[1, 600, 2, 400]$

Review Exercises復習問題

Solution 1解答 1

x-intercept: $(3, 0);$ y-intercept: $(0, −4)$

x切片: $(3, 0);$ y切片: $(0, −4)$

Solution 3解答 3

$y = \frac{5}{3} x + 4$

Solution 5解答 5

$\sqrt{72} = 6 \sqrt{2}$

Solution 7解答 7

$620.097$

Solution 9解答 9

midpoint is $(2, \frac{23}{2})$

中点は $(2, \frac{23}{2})$

Solution 11解答 11

x	y
0	−2
3	2
6	6

A coordinate plane with the x and y axes ranging from -10 to 10. The points (0,-2); (3,2) and (6,6) are plotted and a line runs through all these points.

Solution 13解答 13

$x = 4$

Solution 15解答 15

$x = \frac{12}{7}$

Solution 17解答 17

No solution

解なし

Solution 19解答 19

$y = \frac{1}{6} x + \frac{4}{3}$

Solution 21解答 21

$y = \frac{2}{3} x + 6$

Solution 23解答 23

females 17, males 56

雌17匹、雄56匹

Solution 25解答 25

84 mi

84マイル

Solution 27解答 27

$x = - \frac{3}{4} \pm \frac{i \sqrt{47}}{4}$

Solution 29解答 29

horizontal component $−2;$ vertical component $−1$

横の成分 $−2;$ 縦の成分 $−1$

Solution 31解答 31

$7 + 11 i$

Solution 33解答 33

$16 i$

Solution 35解答 35

$−16 - 30 i$

Solution 37解答 37

$−4 - i \sqrt{10}$

Solution 39解答 39

$x = 7 - 3 i$

Solution 41解答 41

$x = −1, −5$

Solution 43解答 43

$x = 0, \frac{9}{7}$

Solution 45解答 45

$x = 10, −2$

Solution 47解答 47

$x = \frac{- 1 \pm \sqrt{5}}{4}$

Solution 49解答 49

$x = \frac{2}{5}, \frac{- 1}{3}$

Solution 51解答 51

$x = 5 \pm 2 \sqrt{7}$

Solution 53解答 53

$x = 0, 256$

Solution 55解答 55

$x = 0, \pm \sqrt{2}$

Solution 57解答 57

$x = −2$

Solution 59解答 59

$x = \frac{11}{2}, \frac{−17}{2}$

Solution 61解答 61

$(- \infty, 4)$

Solution 63解答 63

$[\frac{- 10}{3}, 2]$

Solution 65解答 65

No solution

解なし

Solution 67解答 67

$(- \frac{4}{3}, \frac{1}{5})$

Solution 69解答 69

Where the blue is below the orange line; point of intersection is $x = 3.5.$

青が橙の線より下にあるところ。交点は $x = 3.5.$

$(3.5, \infty)$

A coordinate plane with the x and y axes ranging from -10 to 10. The lines y = x + 3 and y = 3x -4 graphed on the same axes.

Practice Test実力テスト

Solution 1解答 1

$y = \frac{3}{2} x + 2$

x	y
0	2
2	5
4	8

A coordinate plane with the x and y axes ranging from -10 to 10. The line going through the points (0,2); (2,5); and (4,8) is graphed.

Solution 3解答 3

$(0, −3)$ $(4, 0)$

A coordinate plane with the x and y axes ranging from -10 to 10. The points (4,0) and (0,-3) are plotted with a line running through them.

Solution 5解答 5

$(- \infty, 9]$

Solution 7解答 7

$x = −15$

Solution 9解答 9

$x \neq −4, 2;$ $x = \frac{- 5}{2}, 1$

Solution 11解答 11

$x = \frac{3 \pm \sqrt{3}}{2}$

Solution 13解答 13

$(−4, 1)$

Solution 15解答 15

$y = \frac{−5}{9} x - \frac{2}{9}$

Solution 17解答 17

$y = \frac{5}{2} x - 4$

Solution 19解答 19

$14 i$

Solution 21解答 21

$\frac{5}{13} - \frac{14}{13} i$

Solution 23解答 23

$x = 2, \frac{- 4}{3}$

Solution 25解答 25

$x = \frac{1}{2} \pm \frac{\sqrt{2}}{2}$

Solution 27解答 27

$4$

Solution 29解答 29

$x = \frac{1}{2}, 2, −2$