Deck 2: Linear Equations, Inequalities, and Applications

Question 1

Decide if the statement is .

--4 is a solution of $9 x=-36$ .

Answer 1

True

Question 2

Decide if the statement is .

--2 is a solution of $9 x=-20$ .

Answer 2

False

Question 3

Decide if the statement is .

--1 is a solution of $-3 x-1=2$ .

Answer 3

True

Question 4

Decide if the statement is .

--10 is a solution of $5 x+2=-47$ .

Question 5

Decide if the statement is .

--2 is a solution of $7 x+6 x=-26$ .

Question 6

Decide if the statement is .

--8 is a solution of $2 x-4 x=-47$ .

Question 7

Decide if the statement is .

-4 is a solution of $7 x+3 x=11 x$ .

Question 8

Decide whether the following is an expression or an equation.

- $-3 x+10+10 x+7$

A) Expression
B) Equation

Question 9

Decide whether the following is an expression or an equation.

- $3 x-(2 x-1)=2$

A) Expression
B) Equation

Question 10

Decide whether the following is an expression or an equation.

- $6(6 x+5)=8(9 x-6)$

A) Expression
B) Equation

Question 11

Decide whether the following is an expression or an equation.

- $7(4 x+4)-5(3 x-9)$

A) Expression
B) Equation

Question 12

Decide whether the following is an expression or an equation.

- $-8 x+8-3 x+13=0$

A) Equation
B) Expression

Question 13

Decide whether the following is an expression or an equation.

- $5(2 x-4)=9(x+4)$

A) Equation
B) Expression

Question 14

Decide whether the following is an expression or an equation.

- $-4(x-9)-3(x+4)-4 x$

A) Equation
B) Expression

Question 15

Solve the equation.

- $12 x+9=15$

A) $\left\{\frac{5}{12}\right\}$

B) $\left\{\frac{1}{2}\right\}$

C) $\{2\}$

D) $\left\{-\frac{1}{2}\right\}$

Question 16

Solve the equation.

- $42 \mathrm{~s}+20=12 \mathrm{~s}$

A) $\left\{\frac{10}{27}\right\}$

B) $\left\{-\frac{2}{3}\right\}$

C) $\left\{\frac{3}{2}\right\}$

D) $\left\{\frac{2}{3}\right\}$

Question 17

Solve the equation.

- $39 \mathrm{t}-36=4 \mathrm{t}-6$

A) $\left\{-\frac{13}{14}\right\}$

B) $\left\{-\frac{6}{7}\right\}$

C) $\left\{-\frac{43}{29}\right\}$

D) $\left\{\frac{6}{7}\right\}$

Question 18

Solve the equation.

- $7(x+2)=(7 x+14)$

A) $\{28\}$
B) $\{$ All real numbers $\}$
C) $\{0\}$
D) $\varnothing$

Question 19

Solve the equation.

- $(y-6)-(y+8)=9 y$

A) $\left\{-\frac{7}{3}\right\}$

B) $\left\{-\frac{1}{9}\right\}$

C) $\left\{-\frac{7}{2}\right\}$

D) $\left\{-\frac{14}{9}\right\}$

Question 20

Solve the equation.

- $14(3 c-6)=9 c-3$

A) $\left\{\frac{27}{11}\right\}$

B) $\left\{-\frac{27}{11}\right\}$

C) $\left\{\frac{87}{11}\right\}$

D) $\left\{\frac{9}{17}\right\}$

Question 21

Solve the equation.

- $3(y+8)=4(y-7)$

A) $\{52\}$

B) $\{4\}$

C) $\{-4\}$

D) $\{-52\}$

Question 22

Solve the equation.

- $5 \mathrm{~m}+7+4(3 \mathrm{~m}-3)=3(\mathrm{~m}+3)$

A) $\left\{\frac{7}{10}\right\}$

B) $\{1\}$

C) $\{2\}$

D) $\left\{\frac{2}{7}\right\}$

Question 23

Solve the equation.

- $9 x+2(2 x-2)=18-9 x$

A) $\{1\}$

B) $\left\{\frac{7}{11}\right\}$

C) $\{-1\}$

D) $\left\{\frac{7}{2}\right\}$

Question 24

Solve the equation.

- $-[8 x+(2 x+9)]=8-(5 x+4)$

A) $\left\{-\frac{13}{5}\right\}$

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

C) $\{-3\}$

D) $\{-13\}$

Question 25

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $12 m+4=2(4 m-4)$

A) Conditional; $\{-3\}$
B) Contradiction; $\varnothing$
C) Conditional; $\{1\}$
D) Identity; {all real numbers}

Question 26

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $2(12 t+8)=4(4 t+2)$

A) Conditional; $\{-1\}$
B) Conditional; $\{-3\}$
C) Contradiction; $\varnothing$
D) Identity; {all real numbers}

Question 27

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $5(2 \mathrm{f}-31)=10 \mathrm{f}-155$

A) Conditional; $\{0\}$
B) Contradiction; $\varnothing$
C) Identity; {all real numbers}
D) Identity; $\varnothing$

Question 28

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $4(4 g+17)-16 g-68=0$

A) Conditional; $\{4\}$
B) Identity; {all real numbers}
C) Conditional; $\{0\}$
D) Contradiction; $\varnothing$

Question 29

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

A) Conditional; $\{3\}$
B) Contradiction; $\varnothing$
C) Identity; {all real numbers}
D) Conditional; $\{-3\}$

Question 30

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $-15 s+130+5(3 s-25)=0$

A) Identity; {all real numbers}
B) Contradiction; $\varnothing$
C) Conditional; $\{1\}$
D) Conditional; $\{3\}$

Question 31

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $3 x+8(x+1)+4=12-4 x$

A) Contradiction; $\varnothing$
B) Identity; {all real numbers}
C) Conditional; $\{1\}$
D) Conditional; $\{0\}$

Question 32

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.

- $2[3-(2-5 r)]-r=-4+3(2+3 r)$

A) Identity; {all real numbers}
B) Conditional; $\{4\}$
C) Contradiction; $\varnothing$
D) Conditional; $\{-2\}$

Question 33

Solve the equation.

- $\frac{\mathrm{f}}{4}-3=1$

A) $\{-16\}$

B) $\{16\}$

C) $\{-8\}$

D) $\{8\}$

Question 34

Solve the equation.

- $\frac{p}{4}-\frac{3 p}{8}=3$

A) $\{-21\}$

B) $\{-24\}$

C) $\{21\}$

D) $\{24\}$

Question 35

Solve the equation.

- $\frac{r+6}{5}=\frac{r+8}{7}$

A) $\{-1\}$

B) $\{1\}$

C) $\{2\}$

D) $\{-2\}$

Question 36

Solve the equation.

- $\frac{a}{4}-\frac{1}{4}=-5$

A) $\{-19\}$

B) $\{21\}$

C) $\{-21\}$

D) $\{19\}$

Question 37

Solve the equation.

- $\frac{y}{12}+9=14$

A) $\{-62\}$

B) $\{-60\}$

C) $\{60\}$

D) $\{62\}$

Question 38

Solve the equation.

- $\frac{b}{14}-4=-2$

A) $\{30\}$

B) $\{-28\}$

C) $\{28\}$

D) $\{-30\}$

Question 39

Solve the equation.

- $\frac{7 x+3}{3}+2=-\frac{2 x}{7}$

A) $\left\{-\frac{21}{55}\right\}$

B) $\left\{-\frac{63}{55}\right\}$

C) $\left\{-\frac{63}{43}\right\}$

D) $\left\{\frac{21}{55}\right\}$

Question 40

Solve the equation.

- $0.08x+0.13(x+1800)=360$

A) $\{6000\}$
B) $\{60\}$
C) $\{60,000\}$
D) $\{600\}$

Question 41

Solve the equation.

- $0.06y+0.09(5000-y)=0.22 y$

A) $\{112.5\}$

B) $\{1125\}$

C) $\{5400\}$

D) $\{1800\}$

Question 42

Solve the equation.

- $-0.5(30,000)+0.15 \mathrm{p}=0.02(30,000+\mathrm{p})$

A) $\{2028\}$

B) $\{20,280\}$

C) $\{1,200,000\}$

D) $\{120,000\}$

Question 43

$2 x-5=5+7 x-3$
Is this a linear equation?

Question 44

If one step in the solution of an equation is $57=-3$ , what is the final solution of the equation?

Question 45

This pair of equations is equivalent. $5 x-7=3$ and $8 x+6=22$

Question 46

The solution set of the equation $7 y-6=7 y+3$ is $\{0\}$ . Explain.

Question 47

The solution set of the equation $7(6 s-5)=42 s-35$ is $\{1\}$ . Explain.

Question 48

Find all values of $s$ that make this statement true: $4(2 s-5)=8 s-20$ .

Question 49

Solve the equation for the specified variable. Use the distributive property to factor as necessary.

- $-6 k+a r=r-9 y$ for $r$

A) $r=\frac{-6 k+a}{1-9 y}$ or $r=\frac{6 k-a}{9 y-1}$

B) $r=\frac{6 k-9 y}{a-1}$ or $r=\frac{-6 k+9 y}{1-a}$

C) $r=\frac{a-1}{6 k-9 y}$ or $r=\frac{1-a}{-6 k+9 y}$

D) $r=\frac{-6 k+9 y}{a-1}$ or $r=\frac{6 k-9 y}{1-a}$

Question 50

Solve the equation for the specified variable. Use the distributive property to factor as necessary.

- $9 s+7 p=t p-7$ for $p$

A) $p=\frac{9 s+7}{7}$ or $p=\frac{-9 s-7}{-7}$

B) $\mathrm{p}=\frac{9 \mathrm{~s}+7}{-\mathrm{t}}$ or $\mathrm{p}=\frac{-9 \mathrm{~s}-7}{\mathrm{t}}$

C) $\mathrm{p}=\frac{7-\mathrm{t}}{-9 \mathrm{~s}-7}$ or $\mathrm{p}=\frac{\mathrm{t}-7}{9 \mathrm{~s}+7}$

D) $p=\frac{-9 s-7}{7-t}$ or $p=\frac{9 s+7}{t-7}$

Question 51

Solve the equation for the specified variable. Use the distributive property to factor as necessary.

- $w=\frac{7 y-x}{y}$ for $y$

A) $y=\frac{7-x}{w}$ or $y=\frac{x-7}{-w}$

B) $y=\frac{w-7}{-x}$ or $y=\frac{7-w}{x}$

C) $y=\frac{x}{w-7}$ or $y=\frac{-x}{7-w}$

D) $y=\frac{-x}{w-7}$ or $y=\frac{x}{7-w}$

Question 52

Solve the equation for the specified variable. Use the distributive property to factor as necessary.

- $c=\frac{9 t+4}{t}$ for $t$

A) $\mathrm{t}=\frac{4}{\mathrm{c}-9}$ or $\mathrm{t}=\frac{-4}{-\mathrm{c}+9}$

B) $t=\frac{13}{c}$ or $t=\frac{-13}{-c}$

C) $\mathrm{t}=\frac{-4}{\mathrm{c}-9}$ or $\mathrm{t}=\frac{4}{-\mathrm{c}+9}$

D) $\mathrm{t}=\frac{\mathrm{c}+9}{4}$ or $\mathrm{t}=\frac{-\mathrm{c}-9}{-4}$

Question 53

Solve the equation for $y$ .

- $7 x+2 y=5$

A) $y=\frac{5+7 x}{2}$

B) $y=\frac{5-7 x}{2}$

C) $y=\frac{-5-7 x}{2}$

D) $y=-14 x+10$

Question 54

Solve the equation for $y$ .

- $-4 x+7 y=8$

A) $y=\frac{8-4 x}{7}$

B) $y=28 x+56$

C) $y=\frac{8+4 x}{7}$

D) $y=\frac{-8-4 x}{7}$

Question 55

Solve the equation for $y$ .

- $3 x-7 y=3$

A) $y=\frac{3+3 x}{-7}$ , or $y=\frac{3 x+3}{7}$

B) $y=\frac{-3-3 x}{-7}$ , or $y=\frac{3 x+3}{7}$

C) $y=\frac{-3+3 x}{-7}$ , or $y=\frac{-3 x+3}{7}$

D) $y=\frac{3-3 x}{-7}$ , or $y=\frac{3 x-3}{7}$

Question 56

Solve the equation for $y$ .

- $-9 x-7 y=2$

A) $y=\frac{-2-9 x}{-7}$ , or $y=\frac{9 x+2}{7}$

B) $y=\frac{-2+9 x}{-7}$ , or $y=\frac{2-9 x}{7}$

C) $y=\frac{2-9 x}{-7}$ , or $y=\frac{9 x-2}{7}$

D) $y=\frac{2+9 x}{-7}$ , or $y=\frac{-9 x-2}{7}$

Question 57

Solve the problem.

-Find the corresponding Celsius temperature for a temperature of $250^{\circ} \mathrm{F}$ . Round to the nearest tenth, if necessary.

A) $392.4^{\circ} \mathrm{C}$
B) $482^{\circ} \mathrm{C}$
C) $135.3^{\circ} \mathrm{C}$
D) $121.1^{\circ} \mathrm{C}$

Question 58

Solve the problem.

-Find the corresponding Fahrenheit temperature for a temperature of $51^{\circ} \mathrm{C}$ . Round to the nearest tenth, if necessary.

A) $149.4^{\circ} \mathrm{F}$
B) $123.8^{\circ} \mathrm{F}$
C) $10.6^{\circ} \mathrm{F}$
D) $46.1^{\circ} \mathrm{F}$

Question 59

Solve the problem.

-What is the perimeter of a rectangle of length $15 \mathrm{ft}$ and width $13 \mathrm{ft}$ ?

A) $112 \mathrm{ft}$
B) $28 \mathrm{ft}$
C) $43 \mathrm{ft}$
D) $56 \mathrm{ft}$

Question 60

Solve the problem.

-What is the area of a square with side $2.2 \mathrm{~cm}$ ?

A) $10 \mathrm{~cm}^{2}$
B) $19.36 \mathrm{~cm}^{2}$
C) $4.84 \mathrm{~cm}^{2}$
D) $4.4 \mathrm{~cm}^{2}$

Question 61

Solve the problem.

-Find the area of a triangle with height $16 \mathrm{~m}$ and base $13 \mathrm{~m}$ .

A) $104 \mathrm{~m}^{2}$
B) $208 \mathrm{~m}^{2}$
C) $416 \mathrm{~m}^{2}$
D) $14.5 \mathrm{~m}^{2}$

Question 62

Solve the problem.

-Find the surface area of a cylinder with a radius of $5 \mathrm{~cm}$ and a height of $30 \mathrm{~cm}$ . Use 3.14 for $\pi$ .

A) $1099 \mathrm{~cm}^{2}$
B) $5652 \mathrm{~cm}^{2}$
C) $973.4 \mathrm{~cm}^{2}$
D) $942 \mathrm{~cm}^{2}$

Question 63

Solve the problem.

-Jay drove $256 \mathrm{~km}$ at an average rate of $64 \mathrm{~km} / \mathrm{hr}$ . How long did the trip take?

A) $5 \mathrm{hr}$
B) $4 \mathrm{hr}$
C) $3 \mathrm{hr}$
D) $\frac{1}{4} \mathrm{hr}$

Question 64

Solve the problem.

-Janet drove $284 \mathrm{~km}$ , and the trip took $4 \mathrm{hr}$ . At what average rate was Janet traveling?

A) $71 \mathrm{~km} / \mathrm{hr}$
B) $\frac{1}{71} \mathrm{~km} / \mathrm{hr}$
C) $72 \mathrm{~km} / \mathrm{hr}$
D) $1136 \mathrm{~km} / \mathrm{hr}$

Question 65

Solve the problem.

-The area of a trapezoid is 80 square feet. If the bases are $7 \mathrm{ft}$ and $13 \mathrm{ft}$ , find the altitude of the trapezoid.

A) $8 \mathrm{ft}$
B) $4 \mathrm{ft}$
C) $1.5 \mathrm{ft}$
D) $16 \mathrm{ft}$

Question 66

Solve the problem.

-A circle has a circumference of $30 \pi \mathrm{m}$ . Find the radius of the circle.

A) $15 \mathrm{~m}$
B) $8 \mathrm{~m}$
C) $30 \mathrm{~m}$
D) $5 \mathrm{~m}$

Question 67

Solve the problem.

-Find the simple interest if $\$ 3700$ is borrowed at $15.7 \%$ for 3 months $(0.25 \mathrm{yr})$ .

A) $\$ 14,522.50$
B) $\$ 145.23$
C) $\$ 58.92$
D) $\$ 2323.60$

Question 68

Solve the problem.

-Find the simple interest if $\$ 3200$ is invested at $11.3 \%$ for 2 years.

A) $\$ 723.20$
B) $\$ 566.37$
C) $\$ 180.80$
D) $\$ 361.60$

Question 69

Solve the problem.

-Find the total amount in an account if $\$ 300$ is invested at $11 \%$ simple interest for 2 years.

A) $\$ 354.55$
B) $\$ 66.00$
C) $\$ 366.00$
D) $\$ 333.00$

Question 70

Solve the problem.

-Find the total amount that must be repaid if $\$ 4100$ is borrowed at $7.2 \%$ simple interest for 3 years.

A) $\$ 4395.20$
B) $\$ 5808.33$
C) $\$ 4985.60$
D) $\$ 885.60$

Question 71

Solve the problem.

-A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

A) $50 \mathrm{ml}$
B) $5 \mathrm{ml}$
C) $0.32 \mathrm{ml}$
D) $3.2 \mathrm{ml}$

Question 72

Solve the problem.

-During one year, the Larsons' real estate bill included $\$ 480$ for local schools. Of this amount, $\$ 130$ went to the high school district. What percent did the Larsons pay to the high school district? Round your answer to two decimal places.

A) $26.88 \%$
B) $35.00 \%$
C) $72.92 \%$
D) $27.08 \%$

Question 73

Solve the problem.

-A mixture of chlorine and water contains a total of 45 gallons of liquid. There are 26 gallons of pure chlorine in the mixture. (i) What percent of the mixture is water? (ii) What percent of the mixture is chlorine? Round your answer to the nearest percent, if necessary.

A) (i) $42 \%$ water;(ii) $58 \%$ chlorine
B) (i) $64 \%$ water;(ii) $36 \%$ chlorine
C) (i) $58 \%$ water;(ii) $42 \%$ chlorine
D) (i) $26 \%$ water;(ii) $74 \%$ chlorine

Question 74

Solve the problem.

-The graph shows the percent of students at a local high school who were enrolled in a foreign language class each school year during the 1980s.

What is the best estimate for the number of students taking a language in 1982 if a total of 2630 students were enrolled in the school?

A) 2233 students
B) 66 students
C) 2183 students
D) 447 students

Question 75

Solve the problem.

-The graph shows the percent of students at a local high school who were enrolled in a foreign language class each school year during the 1980s.

What is the best estimate for the number of students not taking a language in 1981 if a total of 2030 students were enrolled in the school?

A) 711 students
B) 661 students
C) 1320 students
D) 3248 students

Question 76

Solve the problem.

-When a loan scheduled to run $n$ payments is paid off $k$ payments ahead of schedule, the amount of unearned interest $\mathrm{u}$ is given by $\mathrm{u}=\mathrm{f} \cdot \frac{\mathrm{k}(\mathrm{k}+1)}{\mathrm{n}(\mathrm{n}+1)}$ , where $\mathrm{f}$ is the total scheduled finance charge. The finance charge on a loan taken out by Ximena is $\$ 668$ . If there were 24 equal monthly installments needed to repay the loan, and the loan is paid in full with 15 months remaining, find the amount of unearned interest. (Round your answer to the nearest cent.)

A) $\$ 87.13$
B) $\$ 267.20$
C) $\$ 100.20$
D) $\$ 254.13$

Question 77

Solve the problem.

-When a loan scheduled to run $n$ payments is paid off $k$ payments ahead of schedule, the amount of unearned interest $\mathrm{u}$ is given by $\mathrm{u}=\mathrm{f} \cdot \frac{\mathrm{k}(\mathrm{k}+1)}{\mathrm{n}(\mathrm{n}+1)}$ , where $\mathrm{f}$ is the total scheduled finance charge. The finance charge on a loan taken out by Ivan is $\$ 414$ . If there were 48 equal monthly installments needed to repay the loan, and the loan is paid in full with 13 months remaining, find the total finance charge paid. (Round your answer to the nearest cent.)

A) $\$ 221.79$
B) $\$ 414.00$
C) $\$ 381.96$
D) $\$ 32.04$

Question 78

Solve the problem.

-The formula $\mathrm{A}=\frac{2400 \mathrm{f}}{\mathrm{b}(\mathrm{p}+1)}$ gives the approximate annual interest rate for a consumer loan paid off with monthly payments, where $f$ is the finance charge on the loan, $p$ is the number of payments, and $b$ is the original amount of the loan. Find the approximate annual interest rate for an automobile loan to be repaid in 24 monthly installments if the finance charge on the loan is $\$ 557$ and the original loan balance is $\$ 3590$ . (Round your answer to two decimal places, if necessary.)

A) $14.89 \%$
B) $16.19 \%$
C) $13.59 \%$
D) $15.51 \%$

Question 79

Solve the problem.

-Students at East Central High School earned $\$ 228$ selling candles. They want to make $\$ 4090$ for a club trip. What percent of their goal has been reached? Round to the nearest tenth of a percent, if necessary.

A) $179 \%$
B) $17.9 \%$
C) $0.6 \%$
D) $5.6 \%$

Question 80

Solve the problem.

-Thompson's Hardware spent $\$ 49,170$ this year on utility costs alone. If total sales were $\$ 258,800$ , what percent of total sales was spent on utility costs? Round to the nearest tenth of a percent, if necessary.

A) $19 \%$
B) $5.3 \%$
C) $1.9 \%$
D) $53 \%$