Deck 3: Solving Equations

Question 1

Write the sentence as an equation with x as the input, or independent, variable and y as the output, or dependent, variable. The output is five less than seven times the input.

A) y = 7x + 5
B) y = 7x - 5
C) y = 5x - 7
D) y = 5 - 7x
E) y = 5 < 7x

Answer 1

y = 7x - 5

Question 2

Tell whether or not the equation is linear. $$y = 4$$

A) Linear
B) Not linear

Answer 2

Linear

Question 3

Write the following problem as an equation and solve. The product of 4 and a number is 24.

A) $24 x = 4$ ; $\frac { 1 } { 6 }$
B) $24 x = 4$ ; 6
C) $4 x = 24$ ; $\frac { 1 } { 6 }$
D) $4 x = 24$ ; 6
E) $24 x = 4$ ; 5

Answer 3

$4 x = 24$ ; 6

Question 4

Write the following problem as an equation and solve. A number decreased by 3 is 2.

A) $x - 3 = 2$ ; 1
B) $x + 2 = 3$ ; 5
C) $x - 3 = 2$ ; 5
D) $x - 2 = 3$ ; 1
E) $x - 3 = 2$ ; -1

Question 5

Write the equation as a sentence: x + 4 = -10.

A) The difference between a number and 4 is -10.
B) The product of a number and 4 is -10.
C) The quotient of a number and 4 is -10.
D) The difference between 4 and a number is -10.
E) The sum of a number and 4 is -10.

Question 6

Write the equation. Let x be the unknown number. Twelve is 7 less than twice a number.

A) 12 = 7 - 2x
B) 12 = 7 < 2x
C) 12 = 2x + 7
D) 12 = 2x - 7
E) 12 = 2(7 - x)

Question 7

Solve the equation from the table. $$11 - x = 10$$ $x \quad y = 11 - x$
1
10
2
9
3
8
4
7

A) $x = 1$
B) $x = 12$
C) $x = 4$
D) $x = 3$
E) $x = 21$

Question 8

Write the equation as a sentence: $\frac { 3 } { 4 } x = 24$

A) Three-fourths times 24 is a number.
B) Three-fourths of a number is 24.
C) Three-fourths of 24 is a number.
D) Three times a number less 4 is 24.
E) The quotient of $\frac { 3 } { 4 }$ and a number is 24.

Question 9

Solve the equation from the table. $$- 4 - 4 x = - 20$$
$\begin{array}{ cc} \text { x } & \text { y=-4-4x} \\1& -8\\2& -12\\3&-16\\4&-20 \\\end{array}$

A) $x = 2$
B) $x = 0$
C) $x = 4$
D) $x = 5$
E) $x = 7$

Question 10

Write the equation for the sentence. Let x be the unknown number. Three times a number is 2.3.

A) 3 + x = 2.3
B) 3 - x = 2.3
C) 3x = 2.3
D) x - 3 = 2.3
E) $\frac { x } { 3 } = 2.3$

Question 11

Write an equation so y depends on x. Find the self-employed Social Security payment, y, at 12.4% of net income, x.

A) x = 0.124y
B) x = 12.4y
C) y = 0.124x
D) y = 12.4x
E) y = 0.0124x

Question 12

Write an equation containing parentheses: The output is the sum of two consecutive numbers.

A) y = x + (x - 2)
B) y = x + (x + 1)
C) y = x - (x + 3)
D) y = x - (x - 3)
E) y = x + (x + 2)

Question 13

Describe the equation as an identity or a conditional equation. For conditional equations, state the number of variables in the equation. $$y = 2 x + 4$$

A) Conditional, 2
B) Identity
C) Conditional, 1
D) Conditional, 3
E) Conditional, 4

Question 14

Write an equation so that y depends on x. Find the amount of tax, y, for an 8.7% sales tax on a purchase x.

A) y = 0.087x
B) y = 0.87x
C) x = 0.87y
D) x = 8.7y
E) y = 8.7x

Question 15

Write the sentence as a two variable equation containing parentheses. Describe your variables so y depends on x. A DVD rental is $7 for two days and a penalty of $8 for each additional day.

A) y = 7 for $x \leq 2$ days; y = 7 +8(x - 2) for x > 2
B) y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1
C) y = 7 for $x \leq 2$ days; y = 7 +(8 - 1)x for x > 2.
D) y = 7 for $x \leq 2$ days; y = 8 +7(x - 2) for x > 2.
E) y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1.

Question 16

Write the following problem as an equation and solve. The sum of a number and 1 is 6.

A) $x + 1 = 6$ ; -5
B) $x + 6 = 1$ ; 5
C) $x + 6 = 1$ ; -5
D) $x + 1 = 6$ ; 5
E) $x + 1 = 6$ ; 3

Question 17

Write the sentence as an equation with x as the input, or independent, variable and y as the output, or dependent, variable. The output is five more than negative two times the input.

A) y = 2x + 5
B) y = 5x + 2
C) y = 5x - 2
D) y = -2x - 5
E) y = -2x + 5

Question 18

Write the sentence as a two-variable equation containing parentheses. Describe your variables so y depends on x. The total cost of an air-compressor rental is $47 for the first day plus $33 for each additional day.

A) y = 47 for x = 1; y = 47 + (33 - 1)x for x > 1
B) y = 47 for x = 1; y = 47 + 33(x + 1) for x > 1
C) y = 47 for x = 1; y = 47 + 33(x - 1) for x > 1
D) y = 33 for x = 1; y = 33 + 47(x - 1) for x > 1
E) y = 47 for x = 1; y = 47 + 33x for x > 1

Question 19

Write the equation. Let x be the unknown number. Eight is three more than two times a number.

A) 8 = 3x + 2
B) 8 = 3x - 2
C) 8 = 3 > 2x
D) 8 = 2x - 3
E) 8 = 2x + 3

Question 20

Solve the equation from the table. $$6 - 2 x = 2$$
$\begin{array}{ cc} \text { x } & \text { y=6-2 x} \\1& 4\\2& 2\\3& 0\\4&-2 \\\end{array}$

A) $x = 7$
B) $x = 5$
C) $x = 2$
D) $x = 3$
E) $x = 4$

Question 21

Solve. $5 + x = 9$

A) 45
B) -4
C) 4
D) 14
E) -5

Question 22

State the inverse operation needed to solve the equation. Solve the equation. $$x - \frac { 7 } { 9 } = 15$$

A) Add $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$
B) Subtract $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$
C) Add $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$
D) Subtract $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$
E) Add $\frac { 7 } { 9 }$ ; x = $13 \frac { 7 } { 9 }$

Question 23

Solve the equation from the table. $$- 12 - 3 x = - 21$$
$\begin{array}{ cc} \text { x } & \text { y=-12-3 x} \\1& -15\\2& -18\\3& -21\\4&-24 \\\end{array}$

A) $x = - 5$
B) $x = - 14$
C) $x = - 10$
D) $x = - 8$
E) $x = 3$

Question 24

Use two calculators tables to solve the equation. $$12 ( x + 2 ) = 14 x + 20$$

A) x = 2
B) x = 1
C) x = 0
D) x = 3
E) x = 4

Question 25

Use two calculators tables to solve the equation. $$6 ( x + 1 ) = 7 x - 9$$

A) x = 16
B) x = 15
C) x = 17
D) x = 14
E) x = 13

Question 26

Use a calculator graph to solve the equation. $$9 x - 8 ( x + 2 ) = 8 ( x + 1 ) - 7 x$$

A) x = 1
B) x = 3
C) x = 8
D) x = 4
E) { }, empty set, no real-number solution; the lines are parallel

Question 27

State the inverse operation needed to solve the equation. Solve the equation. $x + 2 = 6$

A) Subtract 2; x = 4
B) Subtract 2; x = 5
C) Subtract 2; x = 2
D) Add 2; x = 4
E) Add 2; x = 5

Question 28

Solve. $z - 4 = 10$

A) -4
B) -14
C) 6
D) 14
E) -6

Question 29

Solve. $x + 15 = 7$

A) -8
B) 8
C) 7
D) -22
E) 22

Question 30

Use a calculator graph to solve the equation. $$8 x + 10 = 10 x - 8$$

A) x = 9
B) x = 10
C) x = 8
D) x = 11
E) { }, empty set, no real-number solution; the lines are parallel

Question 31

State the inverse operation needed to solve the equation. Solve the equation. $2 x = 24$

A) Divide by 2; x = 13
B) Divide by 2; x = 12
C) Divide by 2; x = 10
D) Multiply by 2; x = 12
E) Multiply by 2; x = 13

Question 32

Check the "solution" of the equation by substituting the number into the equation. Note any wrong "solution." Explain how to solve the equation correctly. $$3 n = 9 , n = 2$$

A) Multiply by 3. The correct solution is n = 3.
B) Divide by 3. The correct solution is n = 3.
C) The solution is correct.
D) Divide by 3. The correct solution is n = 5.
E) Multiply by 3. The correct solution is n = 5.

Question 33

Tell what was done to the first equation to get the second equation. $$5 x = 35 ; x = 7$$

A) Both sides of the first equation were divided by 5.
B) Both sides of the first equation were multiplied by 5.
C) 28 was added to both sides of the first equation.
D) 28 was subtracted from both sides of the first equation.
E) Both sides of the first equation were divided by 7.

Question 34

Solve. $m - 9 = - 7$

A) 7
B) -2
C) 16
D) 2
E) 9

Question 35

Use two calculators tables to solve the equation. $$- 1 ( x - 6 ) = 3 ( x - 5 )$$

A) x = 6.25
B) x = -5.25
C) x = 5.25
D) x = 4.25
E) x = -4.25

Question 36

Use a calculator graph to solve the equation. $$2 ( x + 2 ) = 3 x - 1$$

A) x = 7
B) x = 5
C) x = 4
D) x = 3
E) { }, empty set, no real-number solution; the lines are parallel

Question 37

Solve. $- 7 t = 56$

A) -392
B) 8
C) 49
D) -8
E) 63

Question 38

Use a calculator graph to solve the equation. $$2 ( x - 1 ) = 10 x - 2$$

A) x = -1
B) x = 10
C) x = 0
D) x = 8
E) x = -2

Question 39

Use two calculators tables to solve the equation. $$3 - 10 ( x - 8 ) = - 3 - 2 ( x - 13 )$$

A) x = 5.5
B) x = 9.5
C) x = 6.5
D) x = 8.5
E) x = 7.5

Question 40

Tell what was done to the first equation to get the second equation. $$x - 5 = - 2 , x = 3$$

A) 5 was subtracted from both sides of the first equation.
B) 5 was added to both sides of the first equation.
C) Both sides of the first equation were multiplied by 5.
D) Both sides of the first equation were divided by 5.
E) -5 was added to both sides of the first equation.

Question 41

Complete the table for j, k, m, and n. Then chose the correct answer. $$\begin{array} { l l l l l l l } x & 0 & j & k & m & n & 1 \\y = 5 - 5 x & 5 & 4 & 3 & 2 & 1 & 0\end{array}$$

A) j = $\frac { 1 } { 4 }$
B) j = $\frac { 4 } { 5 }$
C) n = $\frac { 1 } { 5 }$
D) n = $\frac { 1 } { 4 }$
E) n = $\frac { 4 } { 5 }$

Question 42

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { 3 } { 5 } x = 3$

A) Multiply by $- \frac { 3 } { 5 } , x = - 5$
B) Multiply by $- \frac { 5 } { 3 } , x = - 5$
C) Multiply by $- \frac { 5 } { 3 } , x = 5$
D) Multiply by $\frac { 5 } { 3 } , x = 5$
E) Multiply by $\frac { 3 } { 5 } , x = - 5$

Question 43

Solve $D = 54 t \text { for } t \text { if } D = 250 \text {. }$

A) $t = 4 \frac { 17 } { 27 }$
B) $t = 5 \frac { 17 } { 27 }$
C) $t = 4 \frac { 23 } { 24 }$
D) $t = \frac { 7 } { 29 }$
E) $t = 5 \frac { 23 } { 24 }$

Question 44

Solve. $3 z = - 15$

A) -45
B) 5
C) -5
D) -12
E) -18

Question 45

Solve. $8 x = 40$

A) -8
B) 5
C) -40
D) 320
E) -5

Question 46

Solve. $5 + 4 x = 17$

A) 3
B) 9
C) 22
D) 12
E) -3

Question 47

Solve. $11 z - 2 = - 101$

A) -99
B) 9
C) -103
D) -9
E) -90

Question 48

The area of a triangle is $A = \frac { 1 } { 2 } b h$ . If A = 7 and h = 2, solve for b.

A) b = 7
B) b = 8
C) b = 14
D) b = 10
E) b = 3.5

Question 49

The sum of three consecutive integers is 243. Write an equation and solve it to find the smallest integer.

A) x + (x + 2) + (x + 4) = 243, x = 79
B) x + (x + 1) + (x + 2) = 243, x = 80
C) (x - 2) + x + (x + 1) = 243, x = 80
D) x + (x + 1) + (x + 2) = 243, x = 81
E) (x - 2) + (x - 1) + x = 243, x = 81

Question 50

Solve. $7 n - 2 = 47$

A) 38
B) -7
C) 7
D) 45
E) 40

Question 51

Solve the equation from the table. $$\begin{array}{cc}\underline { x } &\underline { y = 6 - 3 x}\\1 & 3 \\2 & 0 \\3 & - 3 \\4 & - 6\end{array}$$ $$6 - 3 x = 12$$

A) x = 2
B) x = -2
C) x = 3
D) x = -3
E) x = -7

Question 52

Solve for x. $- 9 = 2 - 2 x$

A) $x = 5 \frac { 1 } { 2 }$
B) $x = 4 \frac { 1 } { 2 }$
C) $x = 3 \frac { 1 } { 2 }$
D) $x = 8 \frac { 1 } { 2 }$
E) $x = 9 \frac { 1 } { 2 }$

Question 53

Complete the table for j, k, m, and n. Then choose the correct answer. $$\begin{array} { c l l l l l l } x & - 2 & j & k & m & - 1 & n \\y = 2 - 4 x & 10 & 9 & 8 & 7 & 6 & 5\end{array}$$

A) $j = - \frac { 5 } { 4 }$
B) $m = - \frac { 3 } { 2 }$
C) $n = - \frac { 3 } { 4 }$
D) $n = - \frac { 5 } { 4 }$
E) $j = - 1 \frac { 2 } { 3 }$

Question 54

Solve the equation from the table. $$\begin{array}{cc}\underline { x } &\underline { y = 8 - 2 x}\\1 & 6 \\2 & 4 \\3 & 2 \\4 & 0\end{array}$$ $$8 - 2 x = 0$$

A) x = 4
B) x = 1
C) x = 2
D) x = 3
E) x = 8

Question 55

Solve. $2 w + 8 = 2$

A) 3
B) -3
C) 6
D) -14
E) -6

Question 56

Solve the equation to find the cash advance for a 3% credit card fee. 0.03x = 10.80

A) x = 32.4
B) x = 324
C) x = 36
D) x = 3.6
E) x = 360

Question 57

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { x } { 11 } = 5$

A) Multiply by -11; x = -55
B) Multiply by 11; x = -55
C) Multiply by -11; x = 55
D) Divide by 11; x = 55
E) Divide by -11; x = 55

Question 58

Solve. $4 x + 12 = 0$

A) -16
B) 3
C) -3
D) -12
E) -4

Question 59

Solve. $2 - 9 x = 11$

A) -9
B) 1
C) 9
D) 13
E) -1

Question 60

The equation has a letter other than x as a variable. Solve for the variable. $59 = \frac { 9 } { 5 } C + 32$

A) C = 25
B) C = 15
C) C = 12
D) C = 17
E) C = 10

Question 61

Solve the equation. $$3 ( 3 - x ) = - 5$$

A) $x = - 4 \frac { 2 } { 3 }$
B) $x = 4 \frac { 2 } { 3 }$
C) $x = 2 \frac { 1 } { 3 }$
D) $x = - 2 \frac { 1 } { 3 }$
E) $x = 3 \frac { 2 } { 3 }$

Question 62

Solve. $$18 x + 6 ( x - 5 ) = 118$$

A) $6 \frac { 2 } { 7 }$
B) $6 \frac { 1 } { 3 }$
C) $7 \frac { 1 } { 6 }$
D) $6 \frac { 1 } { 6 }$
E) $7 \frac { 2 } { 7 }$

Question 63

Solve. $$5 x + 25 = 2 x + 4$$

A) x = 29
B) x = -13
C) x = -21
D) x = -28
E) x = -7

Question 64

Solve. $$- 4 + 3 ( x + 10 ) = 8$$

A) x = -18
B) x = -1
C) x = -6
D) x = -5
E) x = -21

Question 65

Solve. $18 x + 4 = 6 x + 6$

A) x = $\frac { 1 } { 6 }$
B) x = $\frac { 1 } { 7 }$
C) x = 6
D) x = 7
E) x = 8

Question 66

Write the sentence as an equation containing parentheses. Solve the equation. At an outdoor concert, the staff adds 4 seats to each row of x seats. There are 25 rows altogether, and there are 1,200 seats altogether. How many seats, x, were in the original rows?

A) $1,200 = 25 ( x + 4 ) ; x = 44 \text { seats }$
B) $1,200 = 25 ( x + 4 ) ; \quad x = 43 \text { seats }$
C) $1200 = 25 ( x + 3 ) ; x = 44 \text { seats }$
D) $1200 = 25 ( x - 3 ) ; x = 44 \text { seats }$
E) $1200 = 25 ( x - 3 ) ; x = 43 \text { seats }$

Question 67

Solve the equation. $$4 ( x + 2 ) = - 14$$

A) $x = 5$
B) $x = - 6.5$
C) $x = - 5.5$
D) $x = 5.5$
E) $x = 6.5$

Question 68

Solve. $$2 x + 6 = 70 - 6 x$$

A) x = 1
B) x = 8
C) x = -56
D) x = 64
E) x = -68

Question 69

To solve 2(7 + 3x) = 3x + 8 from a graph, find the value of x where:

A) y = 2(7 + 3x) intersects y = -4.
B) y = 2(7 + 3x) intersects the horizontal axis.
C) y = 3x + 8 intersects the horizontal axis.
D) y = 14 + 6x intersects y = 3x + 8.
E) y = 3x + 8 intersects y = -4.

Question 70

Solve the equation. $8 x + 5 = 4 ( 1 + x ) + 2$

A) $x = \frac { 7 } { 8 }$
B) $x = \frac { 1 } { 4 }$
C) $x = - \frac { 7 } { 8 }$
D) $x = - \frac { 1 } { 4 }$
E) $x = \frac { 8 } { 7 }$

Question 71

Solve. $$4 ( x - 3 ) + 3 x = 9$$

A) x = 0
B) x = 21
C) x = 3
D) x = 14
E) x = 5

Question 72

Solve the equation. $9 ( x - 6 ) = 8$

A) $x = 5 \frac { 7 } { 8 }$
B) $x = \frac { 8 } { 9 }$
C) $x = 5 \frac { 8 } { 9 }$
D) $x = 6 \frac { 8 } { 9 }$
E) $x = 6 \frac { 2 } { 5 }$

Question 73

Solve. $3 x + 3 ( x - 3 ) = 9$

A) x = 5
B) x = 12
C) x = 6
D) x = 3
E) x = -3

Question 74

Solve the equation. $$\frac { 3 } { 10 } ( 3 - 2 x ) = 3$$

A) $x = - 3.5$
B) $x = - 2.5$
C) $x = 2.5$
D) $x = 3.5$
E) $x = 4.5$

Question 75

Solve the equation. $$2 - 3 ( 3 - x ) = 5$$

A) $x = 3$
B) $x = 4$
C) $x = - 3$
D) $x = 6$
E) $x = - 4$

Question 76

Solve. $11 n - 5 = 6 n - 10$

A) x = -5
B) x = -1
C) x = -10
D) x = 15
E) x = 5

Question 77

To solve 4(1 + 3x) = 4 from a graph, find the value of x where:

A) y = 4(1 + 3x) intersects with y = 0.
B) y = 4(1 + 3x) intersects with y = 1.
C) y = 4(1 + 3x) intersects with y = 2.
D) y = 4(1 + 3x) intersects with y = 3.
E) y = 4(1 + 3x) intersects with y = 4.

Question 78

Write the sentence as an equation containing parentheses. Solve the equation. Skate World charges $90 for 10 children and $8 for each additional child. How many children can be invited on a $170 budget? Let the number of children be x.

A) $100 + 8 ( x - 10 ) = 170 ; x = 20$
B) $90 + 8 ( x - 10 ) = 170 ; \quad x = 10$
C) $90 + 8 ( x - 10 ) = 170 ; \quad x = 20$
D) $100 + 8 ( x - 10 ) = 170 , \quad x = 10$
E) $90 - 8 ( x - 10 ) = 170 ; \quad x = 20$

Question 79

Solve the equation. $$5 ( x + 5 ) = 8$$

A) $x = - 3.2$
B) $x = 3.2$
C) $x = 3.4$
D) $x = - 3.4$
E) $x = 3.8$

Question 80

Solve. $2 - 6 ( x + 3 ) = 2$

A) x = 3
B) x = -3
C) x = -4
D) x = 24
E) x = 18