Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 $M _ { 2 }$ .

Accepted Answer

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)  $M _ { 2 } = \frac { F d ^ { 2 } } { G M _ { 1 } }$ 
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 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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.

Accepted Answer

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)  $R = 10.18 \mathrm { ohms }$ 
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 11

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?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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)  $x = \frac { c } { 2 B + 2 k }$ 
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 14

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

Accepted Answer

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)  $51.8 ^ { \circ } < F < 82.4 ^ { \circ }$ 
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 15

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?

Accepted Answer

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

Question 16

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

Accepted Answer

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)  $r = \frac { G } { 2 d } + 1$ 
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 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

A)  $( - 9 , - 16 )$ 
B)  $( - \infty , 16 ) \cup ( 9 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 7 , \infty )$ 
D)  $( - \infty , - 7 )$ 
E)  $( - \infty , - 16 ) \cup ( - 2 , \infty )$ 
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 20

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

Accepted Answer

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

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

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

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

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

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 $M _ { 2 }$ .

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

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

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

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

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.

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?

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

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

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

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?

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

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

Solve the inequality. $| x | < 5$

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

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

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Exam 2: Equations, Inequalities, and Problem Solving

Solve the equation. 7x−15+6x−10x+9=247 x - 15 + 6 x - 10 x + 9 = 247x−15+6x−10x+9=24

Solve the inequality. −32x≥−18- \frac { 3 } { 2 } x \geq - 18−23​x≥−18

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

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

The masses of two objects are M1M _ { 1 }M1​ and M2M _ { 2 }M2​ . The force of gravitation F between the masses is given by F=GMM2d2F = \frac { G M M _ { 2 } } { d ^ { 2 } }F=d2GMM2​​ where GGG is a constant and ddd is the distance between them. Solve for M2M _ { 2 }M2​ .

Solve the inequality. Use interval notation to describe the solution. 3≤−7x+10≤173 \leq - 7 x + 10 \leq 173≤−7x+10≤17

Solve the equation. h7+h8=1\frac { h } { 7 } + \frac { h } { 8 } = 17h​+8h​=1

Use a property of equality to solve the equation. y18=−8\frac { y } { 18 } = - 818y​=−8

Solve the inequality and express the solution set using interval notation. 5(z+7)−3(z−5)>−25 ( z + 7 ) - 3 ( z - 5 ) > - 25(z+7)−3(z−5)>−2

The power PPP lost when an electric current III passes through a resistance RRR is given by the formula P=I2RP = I ^ { 2 } RP=I2R . Solve for RRR . If PPP is 2,900 watts and III is 16 amperes, calculate RRR to the nearest hundredth of an ohm.

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?

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

Solve the formula c=12(B+k)xc = \frac { 1 } { 2 } ( B + k ) xc=21​(B+k)x for the variable xxx .

To hold the temperature of a room between 11∘C11 ^ { \circ } \mathrm { C }11∘C and 28∘C28 ^ { \circ } \mathrm { C }28∘C what Fahrenheit temperatures must be maintained?

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?

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

Use a property of equality to solve the equation. 43=−173+x\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x34​=−317​+x

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

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

Solve A = P + Prt for A , given that P = $1100, r=712%r = 7 \frac { 1 } { 2 } \%r=721​% , and t = 11 years.

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

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

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 $M _ { 2 }$ .

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

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

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

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

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.

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

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

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

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

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

Solve the inequality. $| x | < 5$

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

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