Deck 1: Equations and Inequalities

Question 1

Graph the equation.
The y-value is three more than four times the x-value.

A) $y = 4 x + 3$

B) $y = - 4 x + 3$

C) $y = - 4 x - 3$

D) $y = 4 x - 3$

Answer 1

A

Question 2

Graph the equation.
$$y = \frac { 1 } { x }$$

A)

B)

C)

D)
Write the English sentence as an equation in two variables. Then graph the equation.

Answer 2

A

Question 3

Graph the equation.
$$y = - | x | - 7$$

A)

B)

C)

D)

Answer 3

A

Question 4

Graph the equation.
y = -4

A)

B)

C)

D)

Question 5

Plot the given point in a rectangular coordinate system.
(-3, -5)

A)

B)

C)

D)

Question 6

Graph the equation.
y = 4x - 4

A)

B)

C)

D)

Question 7

Graph the equation.
y = x + 3

A)

B)

C)

D)

Question 8

Plot the given point in a rectangular coordinate system.
(0, 3)

A)

B)

C)

D)

Question 9

Interpret Information About a Graphing Utility's Viewing Rectangle or Table

A)[-2, 16, 2] by [-8, 10, 2]
B)[-2, 16, 2] by [-2, 16, 2]
C)[-8, 10, 2] by [-2, 16, 2]
D)[-20, 10, 2] by [-20, 10, 2]

Question 10

Plot the given point in a rectangular coordinate system.
(-5, 1)

A)

B)

C)

D)

Question 11

Plot the given point in a rectangular coordinate system.
$\left(-4,-\frac{3}{2}\right)$

A)

B)

C)

D)

Question 12

Graph the equation.
$$y = - \frac { 1 } { 4 } x - 2$$

A)

B)

C)

D)

Question 13

Graph the equation.
$y=x^{2}-5$

A)

B)

C)

D)

Question 14

Plot the given point in a rectangular coordinate system.
$$\left( - \frac { 7 } { 2 } , 0 \right)$$

A)

B)

C)

D)

Question 15

Plot the given point in a rectangular coordinate system.
(5, 0)

A)

B)

C)

D)

Question 16

Graph the equation.
The y-value is five decreased by the square of the x-value.

A) $y = 5 - x ^ { 2 }$

B) $y = 5 - x$

C) $y = x ^ { 2 } - 5$

D) $y = x - 5$

Question 17

Plot the given point in a rectangular coordinate system.
(2, -3)

A)

B)

C)

D)

Question 18

Graph the equation.
$y=-3|x|$

A)

B)

C)

D)

Question 19

Graph the equation.
$y=x^{3}-2$

A)

B)

C)

D)

Question 20

Plot the given point in a rectangular coordinate system.
(2, 5)

A)

B)

C)

D)

Question 21

Solve Linear Equations in One Variable
6x - 6 = 54 A) $\{ 10 \}$
В) $\{ 54 \}$
C) $\{ 58 \}$
D) $\{ 15 \}$

Question 22

The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve. $$\begin{array} { | r | c | r | } \hline X & Y _ { 1 } & Y _ { 2 } \\\hline - 3 & 9 & - 3 \\- 2 & 4 & - 1 \\- 1 & 1 & 1 \\0 & 0 & 3 \\1 & 1 & 5 \\2 & 4 & 7 \\3 & 9 & 9 \\\hline\end{array}$$
For which values of $x$ is $Y _ { 1 } = Y _ { 2 }$ ?

A) $- 1$ and 3
B) 2 and 3
C) $- 1$ and 2
D) 2 and $- 3$

Question 23

The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve. $$\begin{array} { | r | c | r | } \hline X & Y _ { 1 } & Y _ { 2 } \\\hline - 3 & 9 & - 3 \\- 2 & 4 & - 1 \\- 1 & 1 & 1 \\0 & 0 & 3 \\1 & 1 & 5 \\2 & 4 & 7 \\3 & 9 & 9 \\\hline\end{array}$$
Does the graph of Y2 pass through the origin?

A)No
B)Yes

Question 24

Use the graph to determine the x- and y-intercepts.

A)x-intercepts: -8, 8; y-intercepts: -2, 2
B)x-intercepts: -8, 8
C)y-intercepts: -2, 2
D)x-intercepts: -2, 2; y-intercepts: -8, 8

Question 25

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

What temperature was recorded at 10 a.m.?

A)73 ° F
B)75 ° F
C)71 ° F
D)74 ° F

Question 26

Use the graph to determine the x- and y-intercepts.

A)x-intercept: -1; y-intercept: 8
B)x-intercept: 1; y-intercept: 8
C)x-intercept: -1; y-intercept: -8
D)x-intercept: -8; y-intercept: 8

Question 27

Interpret Information About a Graphing Utility's Viewing Rectangle or Table

A)[-10, 10, 5] by [-200, 200, 20]
B)[-40, 40, 10] by [-10, 10, 5]
C)[-10, 10, 5] by [-10, 10, 5]
D)[-50, 50, 5] by [-50, 50, 5]

Question 28

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

During which hour did the temperature increase the most?

A)10 a.m. to 11 a.m.
B)1 p.m. to 2 p.m.
C)12 p.m. to 1 p.m.
D)9 a.m. to 10 a.m.

Question 29

The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve. $$\begin{array} { | r | c | r | } \hline X & Y _ { 1 } & Y _ { 2 } \\\hline - 3 & 9 & - 3 \\- 2 & 4 & - 1 \\- 1 & 1 & 1 \\0 & 0 & 3 \\1 & 1 & 5 \\2 & 4 & 7 \\3 & 9 & 9 \\\hline\end{array}$$
At which points do the graph of $Y _ { 1 }$ and $Y _ { 2 }$ intersect?

A) $( - 1,1 )$ and $( 3,9 )$
B) $( - 3 , - 3 )$ and $( - 3,9 )$
C) $( - 1,1 )$ and $( - 3 , - 3 )$
D) $( - 3,9 )$ and $( 3,9 )$

Question 30

Use the graph to determine the x- and y-intercepts.

A)x-intercept: 1; y-intercept: -1
B)x-intercept: 1; y-intercept: 1
C)x-intercept: -1; y-intercept: -1
D)x-intercept: -1; y-intercept: 1

Question 31

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

At what time was the temperature its lowest?

A)9 a.m.
B)6 p.m.
C)4 p.m.
D)1 p.m.

Question 32

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

At what time was the temperature the highest?

A)1 p.m.
B)5 p.m.
C)11 a.m.
D)2 p.m.

Question 33

Use the graph to determine the x- and y-intercepts.

A)x-intercepts: 2, 1, 5; y-intercept: -2
B)x-intercept: -2; y-intercepts: 2, 1, 5
C)x-intercepts: -2, 1, -5; y-intercept: -2
D)x-intercept: -2; y-intercepts: -2, 1, -5

Question 34

Interpret Information About a Graphing Utility's Viewing Rectangle or Table

A)[-10, 30, 10] by [-400, 500, 100]
B)[-1, 8, 1] by [-1, 8, 1]
C)[-1, 5, 1] by [-4, 8, 1]
D)[-10, 5, 1] by [-10, 5, 1]

Question 35

Use the graph to determine the x- and y-intercepts.

A)x-intercept: -1
B)y-intercept: -1
C)x-intercept: 1
D)y-intercept: 1

Question 36

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

During which two hour period did the temperature increase the most?

A)9 a.m. to 11 a.m.
B)10 a.m. to 11 a.m.
C)12 p.m. to 2 p.m.
D)10 a.m. to 12 p.m.

Question 37

Use the graph to determine the x- and y-intercepts.

A)x-intercepts: -4, 4; y-intercept: -4
B)x-intercepts: -4, 4
C)y-intercept: -4
D)x-intercepts: -4, 4; y-intercept: 0

Question 38

Use the graph to determine the x- and y-intercepts.

A)x-intercepts: -3, 1; y-intercept: 3
B)x-intercept: -3; y-intercepts: 1, 3
C)x-intercept: 3; y-intercepts: -3, 1
D)x-intercept: 1; y-intercept: 3

Question 39

Interpret Information Given by Graphs
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

At what time was the temperature 79°?

A)1 p.m.
B)4 p.m.
C)12 p.m.
D)3 p.m.

Question 40

The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve. $$\begin{array} { | r | c | r | } \hline X & Y _ { 1 } & Y _ { 2 } \\\hline - 3 & 9 & - 3 \\- 2 & 4 & - 1 \\- 1 & 1 & 1 \\0 & 0 & 3 \\1 & 1 & 5 \\2 & 4 & 7 \\3 & 9 & 9 \\\hline\end{array}$$
Which equation corresponds to $\mathrm { Y } _ { 2 }$ in the table?

A) $y _ { 2 } = 2 x + 3$
B) $\mathrm { y } _ { 2 } = 2 - 3 \mathrm { x }$
C) $y _ { 2 } = x + 2$
D) $\mathrm { y } _ { 2 } = 2 \mathrm { x } - 3$

Question 41

Solve Linear Equations in One Variable
$$( - 5 x + 5 ) + 1 = - 4 ( x + 7 )$$

A) $\{ 34 \}$
B) $\{ - 34 \}$
C) $\{ - 32 \}$
D) $\{ 1 \}$

Question 42

Solve the equation.
$$\frac { 2 x } { 5 } = \frac { x } { 3 } + 3$$

A) $\{ 45 \}$
B) $\{ - 45 \}$
C) $\{ 90 \}$
D) $\{ - 90 \}$

Question 43

Find all values of x satisfying the given conditions.
$y _ { 1 } = 8 x + 4 ( 4 + x ) , y _ { 2 } = 3 ( x - 6 ) + 10 x$ , and $y _ { 1 } = y _ { 2 }$

A) $\{ 34 \}$
B) $\{ 10 \}$
C) $\{ - 34 \}$
D) $\{ - 10 \}$ Find all values of x such that y = 0.

Question 44

Solve the equation.
$$\frac { x + 8 } { 6 } = \frac { 3 } { 2 } - \frac { x - 1 } { 3 }$$

A) $\{ 1 \}$
B) $\{ 10 \}$
C) $\{ 0 \}$
D) $\{ 27 \}$

Question 45

Solve the equation.
$$\frac { x + 6 } { - 3 } + \frac { x + 3 } { 3 } = x - 8$$

A) $\{ 7 \}$
B) $\{ 11 \}$
C) $\{ 5 \}$
D) $\{ 9 \}$

Question 46

Solve the equation.
$$80 - \frac { x } { 9 } = \frac { x } { 7 }$$

A) $\{ 315 \}$
B) $\{ 640 \}$
C) $\left\{ \frac { 1280 } { 63 } \right\}$
D) $\{ 5 \}$

Question 47

Solve Linear Equations in One Variable
$$0.50 x - 0.20 ( 50 + x ) = 0.04 ( 50 )$$

A) $\{ 40 \}$
B) $\{ 30 \}$
C) $\{ 50 \}$
D) $\{ 20 \}$

Question 48

Find all values of x satisfying the given conditions.
$$y = \frac { x + 9 } { 2 } + \frac { x - 1 } { 6 } - 5$$

A) $\{ 1 \}$
B) $\{ 26 \}$
C) $\{ 0 \}$
D) $\{ 60 \}$

Question 49

Solve the equation.
$$\frac { x } { 2 } = \frac { x } { 3 } + \frac { 7 } { 2 }$$

A) $\{ 21 \}$
B) $\left\{ - \frac { 7 } { 2 } \right\}$
C) 0
D) $\left\{ \frac { 1 } { 21 } \right\}$

Question 50

Find all values of x satisfying the given conditions.
$$y = 2 [ 5 x - ( 6 x - 1 ) ] - 7 ( x - 1 )$$

A) $\{ 1 \}$
B) $\{ - 1 \}$
C) $\left\{ \frac { 5 } { 9 } \right\}$
D) $\left\{ - \frac { 5 } { 9 } \right\}$

Question 51

Solve Linear Equations in One Variable
$$- 8 x - 2 = 4 + 2 x$$

A) $\left\{ - \frac { 3 } { 5 } \right\}$
B) $\left\{ - \frac { 5 } { 3 } \right\}$
C) $\left\{ \frac { 5 } { 3 } \right\}$
D) $\{ - 3 \}$

Question 52

Solve Linear Equations in One Variable
$$3 ^ { 2 } - 2 ( 12 - 9 ) ^ { 2 } = 54 x$$

A) $\left\{ - \frac { 1 } { 6 } \right\}$
B) $\{ 6 \}$
C) $\{ 0 \}$
D) $\left\{ \frac { 7 } { 6 } \right\}$

Question 53

Solve Linear Equations in One Variable
$$- 5 x + 1 - 2 ( x + 1 ) = 4 x + 6$$

A) $\left\{ - \frac { 7 } { 11 } \right\}$
B) $\left\{ - \frac { 7 } { 5 } \right\}$
C) $\left\{ - \frac { 9 } { 11 } \right\}$
D) $\left\{ - \frac { 9 } { 5 } \right\}$

Question 54

Solve Linear Equations in One Variable
$$9 x - ( 7 x - 1 ) = 2$$

A) $\left\{ \frac { 1 } { 2 } \right\}$
B) $\left\{ \frac { 1 } { 16 } \right\}$
C) $\left\{ - \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 16 } \right\}$

Question 55

Solve the equation.
$\frac { 2 x } { 7 } - x = \frac { x } { 56 } - \frac { 5 } { 8 }$

A) $\left\{ \frac { 35 } { 41 } \right\}$
B) $\left\{ - \frac { 35 } { 39 } \right\}$
C) $\left\{ \frac { 35 } { 39 } \right\}$
D) $\left\{ - \frac { 35 } { 41 } \right\}$

Question 56

Solve the equation.
$$\frac { x } { 3 } = \frac { x } { 8 } + 6$$

A) $\left\{ \frac { 144 } { 5 } \right\}$
B) $\{ 48 \}$
C) $\{ 18 \}$
D) $\{ 24 \}$

Question 57

Solve Linear Equations in One Variable
0.40(30)+ 0.70x = 0.60(30 + x)

A){60}
B){50}
C){70}
D){30}

Question 58

Solve Linear Equations in One Variable
$$- 4 [ 3 x + 7 + 3 ( x + 1 ) ] = - 7 x - 5$$

A) $\left\{ - \frac { 35 } { 17 } \right\}$
B) $\left\{ \frac { 35 } { 3 } \right\}$
C) $\left\{ \frac { 21 } { 17 } \right\}$
D) $\{ - 7 \}$

Question 59

Find all values of x satisfying the given conditions.
$y _ { 1 } = \frac { x + 6 } { 3 } , y _ { 2 } = \frac { x + 8 } { 6 }$ , and $y _ { 1 } = y _ { 2 }$

A) $\{ - 4 \}$
B) $\{ 4 \}$
C) $\{ - 12 \}$
D) $\{ 3 \}$ Find all values of x such that y = 0.

Question 60

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { 10 } { x } = \frac { 1 } { 2 x } + 38$$

A) $x \neq 0 ; \left\{ \frac { 1 } { 4 } \right\}$
B) $x \neq 0 ; \{ 4 \}$
C) $x \neq 0,2 ; \left\{ \frac { 21 } { 38 } \right\}$
D) No restrictions; $\{ 2 \}$

Question 61

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
3(3x + 6)= 9x + 18

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 62

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { 5 } { x + 1 } + \frac { 2 } { x - 1 } = \frac { 4 } { ( x + 1 ) ( x - 1 ) }$$

A) $x \neq - 1,1$ ; $\varnothing$
B) $x \neq - 1,1 ; \{ 2 \}$
C) $x \neq - 1 ; \{ 1 \}$
D) No restrictions; $\{ 1 \}$

Question 63

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
$$\frac { 2 x } { x } = 2$$

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 64

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
2(x - 3)- 6 = 9x - 7(x - 6)

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 65

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-4x + 6(-2x - 3)= -28 - 6x

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 66

Find all values of x satisfying the given conditions.
$y _ { 1 } = \frac { 1 } { x + 6 } , y _ { 2 } = \frac { 2 } { x + 3 } , y _ { 3 } = \frac { - 3 } { x ^ { 2 } + 9 x + 18 }$ , and $y _ { 1 } + y _ { 2 } = y _ { 3 }$

A) $\{ 0 \}$
B) $\{ - 6 \}$
C) $\{ 3 \}$
D) $\varnothing$

Question 67

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
$$5 x + 3 - 7 x + 4 = 2 x - 4 x + 4$$

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 68

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { 8 } { x } + 4 = \frac { 1 } { 2 x } + \frac { 9 } { 5 }$$

A) $x \neq 0 ; \left\{ - \frac { 75 } { 22 } \right\}$
B) $x \neq 0 ; \left\{ - \frac { 22 } { 75 } \right\}$
C) $x \neq 0,2,5 ; \left\{ - \frac { 75 } { 22 } \right\}$
D) No restrictions; $\left\{ - \frac { 22 } { 75 } \right\}$

Question 69

Solve the equation.
$$\frac { 1 } { x + 4 } + \frac { 2 } { x + 3 } = \frac { - 1 } { x ^ { 2 } + 7 x + 12 }$$

A) $\varnothing$
B) $\{ - 4 \}$
C) $\{ 3 \}$
D) $\{ 0 \}$

Question 70

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
$$\frac { - 2 x + 9 } { 5 } + 1 = - \frac { 4 x } { 5 }$$

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 71

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { x - 6 } { 3 x } + 8 = \frac { x + 5 } { x }$$

A) $x \neq 0 ; \left\{ \frac { 21 } { 22 } \right\}$
B) $x \neq 0 ; \left\{ - \frac { 13 } { 2 } \right\}$
C) $x \neq 0,3 ; \left\{ \frac { 21 } { 22 } \right\}$
D) No restrictions; $\left\{ \frac { 11 } { 24 } \right\}$

Question 72

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
16x + 15(x + 1)= 31(x + 1)- 16

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 73

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { 6 } { 2 x - 2 } + \frac { 1 } { 2 } = \frac { 3 } { x - 1 }$$

A) $x \neq 1 ; \varnothing$
B) $x \neq 2 ; \{ 1 \}$
C) $\mathrm { x } \neq 1 ; \{ 1 \}$
D) $x \neq - 1,2 ; \{ 1,2 \}$

Question 74

Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
$$\frac { 3 } { x - 1 } + 1 = \frac { 7 } { x - 1 }$$

A) $x \neq 1 ; \{ 5 \}$
B) $x \neq - 1 ; \{ 5 \}$
C) $x \neq - 1 ; \{ 11 \}$
D) $x \neq 1 ; \varnothing$

Question 75

Find all values of x satisfying the given conditions.
$y _ { 1 } = \frac { 6 } { x + 3 } , y _ { 2 } = \frac { 8 } { x - 3 } , y _ { 3 } = \frac { 14 } { x ^ { 2 } - 9 }$ , and $y _ { 1 } - y _ { 2 } = y _ { 3 }$

A) $\{ - 28 \}$
B) $\{ 28 \}$
C) $\{ \sqrt { 43 } \}$
D) $\{ 56 \}$

Question 76

Solve the equation.
$$\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$$

A) $\{ 3 \}$
B) $\left\{ \frac { 3 } { 2 } \right\}$
C) $\{ - 3 \}$
D) $\left\{ - \frac { 12 } { 5 } \right\}$

Question 77

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
$$\frac { 2 x } { x - 3 } = \frac { 6 } { x - 3 } + 4$$

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 78

Recognize Identities, Conditional Equations, and Inconsistent Equations
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
2x + 7x = 8x

A)Identity
B)Conditional equation
C)Inconsistent equation

Question 79

Solve the equation.
$\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }$

A) $\{ - 5 \}$
B) $\{ - 40 \}$
C) $\{ 5 \}$
D) $\{ - 8 \}$

Question 80

Solve the equation.
$$\frac { 8 } { y + 4 } - \frac { 6 } { y - 4 } = \frac { 6 } { y ^ { 2 } - 16 }$$

A) $\{ 31 \}$
B) $\{ - 31 \}$
C) $\{ \sqrt { 58 } \}$
D) $\{ 62 \}$