Deck 2: Equations, Inequalities, and Problem Solving

Question 1

Use the properties of equality to solve the equation. $$\frac { 11 } { 12 } a = \frac { 1 } { 3 }$$

A) $a = \frac { 1 } { 12 }$
B) $a = \frac { 4 } { 11 }$
C) $a = \frac { 1 } { 11 }$
D) $a = \frac { 4 } { 3 }$
E)none of these

Answer 1

$a = \frac { 4 } { 11 }$

Question 2

Solve the equation. $$2 x + 4 + 7 x = 3 x + 2 x - 32$$

A)x = -9
B)x = -7
C)x = -13
D)x = 13
E)x = -5

Answer 2

x = -9

Question 3

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

A)t = -36
B)t = 108
C)t = 36
D)t = 72
E)t = 34

Answer 3

t = 36

Question 4

Solve the equation. n + 0.5 n = 90

A)n = 90
B)n = 0.5
C)n = -29.5
D)n = 60
E)n = 149.5

Question 5

Use a property of equality to solve the equation. $$\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$$

A) $5$
B) $7$ .
C) $2$
D) $7$
E) $0$

Question 6

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ".

A)x = 11
B)x = 15
C)x = 6
D)x = 8
E)x = 10

Question 7

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

A)2%
B)6%
C)8%
D)5%
E)3%

Question 8

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4)= 2( x + 5)

A) $x = - \frac { 9 } { 2 }$
B) $x = \frac { 11 } { 2 }$
C) $x = \frac { 5 } { 2 }$
D)identity
E)contradiction

Question 9

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

A)15
B)30
C)25
D)35
E)20

Question 10

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal)of $4,250 has grown to be $4,520?

A)$280
B)$270
C)$255
D)$275
E)$250

Question 11

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

A)$2,500 at 13%, $5,000 at 15%
B)$5,000 at 13%, $7,500 at 15%
C)$5,200 at 13%, $7,300 at 15%
D)$5,200 at 13%, $7,700 at 15%
E)$7,500 at 13%, $5,000 at 15%

Question 12

Solve the equation. 0.43 x + 0.4(8,000 - x )= 3350

A)x = 5,000
B)x = 3,000
C)x = -3,000
D)x = 8,000
E)no solution

Question 13

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$

A) $p = \frac { 2 } { 5 }$
B) $p = \frac { 1 } { 15 }$
C) $p = 1 \frac { 4 } { 15 }$
D) $p = \frac { 11 } { 15 }$
E)none of these

Question 14

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$

A) $h = \frac { 8 } { 15 }$
B) $h = \frac { 15 } { 56 }$
C) $h = \frac { 1 } { 15 }$
D) $h = \frac { 56 } { 15 }$
E)no solution

Question 15

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

A)5 inches wide, 7 inches long
B)2 inches wide, 10 inches long
C)3 inches wide, 9 inches long
D)4 inches wide, 8 inches long
E)7 inches wide, 5 inches long

Question 16

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

A)20 feet
B)4 feet
C)12 feet
D)-4 feet
E)8 feet

Question 17

Use a property of equality to solve the equation. $$\frac { y } { 18 } = - 8$$

A)-147
B)- 152
C)- 153
D)- 137
E)- 144

Question 18

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

A)$64,500
B)$69,500
C)$68,500
D)$67,500
E)$71,500

Question 19

Solve the equation. 5( t - 2)+ 2( t - 1)= -2( t - 1)+ 10( t + 2)

A)t = -44
B)t = -36
C)t = -34
D)t = -29
E)t = -27

Question 20

Solve the equation. $$7 x - 15 + 6 x - 10 x + 9 = 24$$

A)x = 11
B)x = -10
C)x = 3
D)x = 10
E)x = 20

Question 21

The perimeter $P$ of a rectangle with length I and width W is given by the formula $P = 2 l + 2 w$ . Solve this formula for W . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

A) $w = \frac { P - 2 l } { 2 } ; w = 4.83 \mathrm {~m}$
B) $w = \frac { 2 l - P } { 2 } ; w = 7.02 \mathrm {~m}$
C) $w = P - 2 l ; \quad w = 14.04 \mathrm {~m}$
D) $w = \frac { P - 2 l } { 2 } ; w = 7.02 \mathrm {~m}$
E) $w = 2 l - P ; \quad w = 4.83 \mathrm {~m}$

Question 22

Solve the inequality. $$- \frac { 3 } { 2 } x \geq - 18$$

A) $[ 14 , \infty )$
B) $( - \infty , 14 ]$
C) $[ 12 , \infty )$
D) $( - \infty , 12 ]$
E) $( - \infty , 12 )$

Question 23

The masses of two objects are $M _ { 1 }$ and $M _ { 2 }$ . The force of gravitation F between the masses is given by $F = \frac { G M M _ { 2 } } { d ^ { 2 } }$ where $G$ is a constant and $d$ is the distance between them. Solve for $M _ { 2 }$ .

A) $M _ { 2 } = \frac { F } { G M _ { 1 } d ^ { 2 } }$
B) $M _ { 1 } = \frac { F d ^ { 2 } } { G M _ { 2 } }$
C) $M _ { 1 } = \frac { F } { G M _ { 2 } d ^ { 2 } }$
D) $M _ { 2 } = \frac { F G M _ { 1 } } { d ^ { 2 } }$
E) $M _ { 2 } = \frac { F d ^ { 2 } } { G M _ { 1 } }$

Question 24

Solve the formula for B . Volume of a pyramid: $V = \frac { 1 } { 3 } B h$

A) $B = 3 \frac { h } { V }$
B) $B = 3 \mathrm { Vh }$
C) $B = 3 \frac { \mathrm { V } } { \mathrm { h } }$
D) $B = \frac { V } { 3 h }$
E)none of these

Question 25

Solve the inequality. $$4 x + 9 \geq 3 x + 14$$

A) $x > 5$
B) $x \neq 5$
C) $x \geq 5$
D) $x < 5$
E) $x \leq 5$

Question 26

Solve the formula $G = 2 ( r - I ) d$ for the variable $7 ^ { \prime }$ .

A) $r = \frac { 2 G } { d } - 1$
B) $r = \frac { G + 1 } { 2 d }$
C) $= \frac { G } { 2 d } - 1$
D) $r = \frac { 2 G } { d } + 1$
E) $r = \frac { G } { 2 d } + 1$

Question 27

For the following problem, solve the inequality and express the solution set using interval notation. $8 x - 48 - 2 x > 36$

A) $( 15 , \infty )$
B) $( 14 , \infty )$
C) $( 13 , \infty )$
D) $( - 14 , \infty )$
E)none of these

Question 28

Solve the inequality. $4 ( x + 5 ) > 12$

A) $x < - 2$
B) $x \leq - 2$
C) $x = - 2$
D) $x \geq - 2$
E) $x > - 2$

Question 29

Solve the inequality. Write the answer in interval notation. $6 - x < 4 < 7 - x$

A) $( - 3 , - 2 )$
B) $( - \infty , \infty )$
C) $( 2,3 )$
D)no solution

Question 30

Solve the inequality. -2 x ≥ 6

A)x ≥ -3
B)x ≠ -3
C)x ≤ 3
D)x
E)x ≤ -3

Question 31

Solve the formula $V = I T$ for the variable $T$ .

A) $T = \frac { I } { V }$
B) $T = V I$
C) $T = \frac { V } { I }$
D) $\frac { 1 } { T } = \frac { V } { I }$
E) $T = \frac { 1 } { V I }$

Question 32

Solve the formula $i = p r t$ for the variable r . Then substitute numbers i = 90 , p = 200, and t = 5 to find the variable's value.

A)r = 105
B)r = - 115
C)r = 0.09
D)r = 295
E)r = 0.45

Question 33

Solve the formula $$c = \frac { 1 } { 2 } ( B + k ) x$$ for the variable $x$ .

A) $x = \frac { B + k } { 2 c }$
B) $x = \frac { c } { 2 ( B + k ) }$
C) $x = \frac { 2 ( B + k ) } { c }$
D) $x = \frac { 2 c } { B + k }$
E) $x = \frac { c } { 2 B + 2 k }$

Question 34

Solve the inequality and express the solution set using interval notation. $8 ( 7 - x ) \leq 10 ( 7 - x )$

A) $[ 8 , \infty )$
B) $( - \infty , 8 ]$
C) $[ 7 , \infty )$
D) $( - \infty , 7 ]$
E) $[ 7 , \infty ]$

Question 35

Solve the compound inequality. Graph the solution set (if one exists)and write it using interval notation. $- 3 x < - 4 x$ and $9 x > 8 x$

A) $( - \infty , 0 ) \cup ( 0 , \infty )$
B) $x = 0$
C) $( - \infty , 0 )$
D) $( 0 , \infty )$
E) $\phi$

Question 36

Solve the inequality. Graph the result. $$\frac { 1 } { 4 } x - \frac { 1 } { 3 } \leq x + 2$$

A)
B)
C)
D)
E)

Question 37

Solve the inequality and express the solution set using interval notation. $5 ( z + 7 ) - 3 ( z - 5 ) > - 2$

A)(- ?, -26)
B)(-26, ?)
C)(- ?, -11)
D)(-11, ?)
E)(26, ?)

Question 38

Graph the solution set. $$0.4 > 3 x - 0.02$$

A)
B)
C)
D)
E)

Question 39

Solve A = P + Prt for A , given that P = $1100, $r = 7 \frac { 1 } { 2 } \%$ , and t = 11 years.

A)A = $2,057.50
B)A = $2,007.50
C)A = $907.50
D)A = $2,307.50
E)A = $1,907.50

Question 40

The power $P$ lost when an electric current $I$ passes through a resistance $R$ is given by the formula $P = I ^ { 2 } R$ . Solve for $R$ . If $P$ is 2,900 watts and $I$ is 16 amperes, calculate $R$ to the nearest hundredth of an ohm.

A) $R = 11.33 \mathrm { ohms }$
B) $R = 9.28 \text { ohms }$
C) $R = 12.18 \mathrm { ohms }$
D) $R = 181.25 \text { ohms }$
E) $R = 10.18 \mathrm { ohms }$

Question 41

Solve the inequality. $$| x | < 5$$

A) $( - 5,5 )$
B) $( 0,5 )$
C) $( - 5,0 ) \cup ( 0,5 )$
D) $( - 5,0 )$
E) $[ - 5,5 ]$

Question 42

Solve the equation. $$| x + 9 | > 7$$

A) $( - 9 , - 16 )$
B) $( - \infty , 16 ) \cup ( 9 , \infty )$
C) $( - \infty , - 2 ) \cup ( - 7 , \infty )$
D) $( - \infty , - 7 )$
E) $( - \infty , - 16 ) \cup ( - 2 , \infty )$

Question 43

Solve the problem by setting up and solving an appropriate inequality. Sue bowled 150 and 140 in her first two games. What must she bowl in the third game to have an average of at least 170 for the three games?

A) $x \geq 240$
B) $x \geq 220$
C) $x \leq 220$
D) $x > 220$
E) $x > 240$

Question 44

To hold the temperature of a room between $11 ^ { \circ } \mathrm { C }$ and $28 ^ { \circ } \mathrm { C }$ what Fahrenheit temperatures must be maintained?

A) $50.7 ^ { \circ } < F < 81.3 ^ { \circ }$
B) $54 ^ { \circ } < F < 84.6 ^ { \circ }$
C) $51.8 ^ { \circ } < F < 79.1 ^ { \circ }$
D) $48.5 ^ { \circ } < F < 79.1 ^ { \circ }$
E) $51.8 ^ { \circ } < F < 82.4 ^ { \circ }$

Question 45

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour. ACTION Truck Rental Big $22 \mathrm { ft }$ Truck Only \$26.95 for one hour. $\$ 7.95$ for each extra hour.

A)Approximately 10 hr
B)Approximately 8 hr
C)Approximately 12 hr
D)Approximately 15 hr
E)Approximately 7 hr

Question 46

Solve the equation, if possible. $$| x + 4 | = 12$$

A)8, -16
B)8
C)8, 16
D)-8 , -16
E)no solution

Question 47

Solve the equation, if possible. $$| 5 x + 7 | = - | 9 x - 2 |$$

A) $1 , - 9$
B) $1,9$
C) $- 9 , - 1$
D) $- 5 , - 1$
E)no solution

Question 48

Solve the equation. $$| 3 x - 21 | + 15 = 21$$

A)x = -5, x = 9
B)x = 9
C)x = 5, x = 9
D)x = 5
E)x = -5, x = -9

Question 49

Solve the equation. Give the solution in interval notation. $$| 4 - 5 x | \geq 14$$

A) $( - \infty , - 2 ] \cup \left[ \frac { 18 } { 5 } , \infty \right)$
B) $\left[ \frac { 18 } { 5 } , \infty \right)$
C) $\left[ - 2 , \frac { 18 } { 5 } \right]$
D) $( - \infty , - 2 ]$
E)no solution

Question 50

Solve the inequality. Use interval notation to describe the solution. $3 \leq - 7 x + 10 \leq 17$

A) $[ - 2,1 ]$
B) $[ 0,2 ]$
C) $[ - 1,1 ]$
D) $[ 0,1 ]$
E) $( 0,1 )$