Question 1

Solve using the multiplication principle.
-$\frac{4}{7}>-2 x$

Accepted Answer

A)  $\left\{|x| x>\frac{4}{7}\right\}$ 
B)  $\left\{x \mid x-\frac{2}{7}\right\}$ 
A)  $\left\{|x| x>\frac{4}{7}\right\}$ 
B)  $\left\{x \mid x-\frac{2}{7}\right\}$

Question 2

Solve using the addition and multiplication principles.
-$11 a+2 \geq 12 a+12$

Accepted Answer

A)  $\{a \mid a \leq 11\}$ 
B)  $\{a \mid a \leq-10\}$ 
C)  $\{a \mid a \geq 10\}$ 
D)  $\{\mathrm{a} \mid \mathrm{a}>11\}$ 
A)  $\{a \mid a \leq 11\}$ 
B)  $\{a \mid a \leq-10\}$ 
C)  $\{a \mid a \geq 10\}$ 
D)  $\{\mathrm{a} \mid \mathrm{a}>11\}$

Question 3

Solve. Clear fractions first.
-$\frac{1}{5} r+\frac{6}{5}=\frac{1}{7} r+\frac{8}{7}$

Accepted Answer

A)  1 
B)  2 
C)  -1 
D)  -2 
A)  1 
B)  2 
C)  -1 
D)  -2

Question 4

Solve using the multiplication principle.
-$\frac{5}{7} \mathrm{k}=10$

Accepted Answer

A)  14 
B)  1 
C)  11 
D)  12 
A)  14 
B)  1 
C)  11 
D)  12

Question 5

Solve the problem.
-If three times the smaller of two consecutive integers is added to four times the larger, the result is 88. Find the smaller integer.

Accepted Answer

A)  36 
B)  13 
C)  12 
D)  11 
A)  36 
B)  13 
C)  12 
D)  11

Question 6

Solve using the multiplication principle.
-$\frac{1}{9} x=22$

Accepted Answer

A)  31 
B)  176 
C)  189 
D)  198 
A)  31 
B)  176 
C)  189 
D)  198

Question 7

Solve the problem. Round to the nearest hundredth, if necessary.
-$35 \%$ of what number is 75 ?

Accepted Answer

A)  2142.9 
B)  47 
C)  214.29 
D)  0.47 
A)  2142.9 
B)  47 
C)  214.29 
D)  0.47

Question 8

Solve.
-$4[3-3(x+1)]+1=2(-51-x)+2 x+51$

Accepted Answer

A)  $\frac{13}{3}$ 
B)  13 
C)  $\frac{13}{6}$ 
D)  0 
A)  $\frac{13}{3}$ 
B)  13 
C)  $\frac{13}{6}$ 
D)  0

Question 9

Solve the equation using the addition principle.
-$m+2 \frac{2}{3}=3 \frac{2}{3}$

Accepted Answer

A)  1 
B)  3 
C)  $\frac{19}{3}$ 
D)  $\frac{10}{3}$ 
A)  1 
B)  3 
C)  $\frac{19}{3}$ 
D)  $\frac{10}{3}$

Question 10

Solve the problem.
-Sales of frozen pizza for a club fund-raiser increased from 500 one year to 615 the next year. What was the percent of increase?

Accepted Answer

A)  $81.3 \%$ 
B)  $77 \%$ 
C)  $23 \%$ 
D)  $18.7 \%$ 
A)  $81.3 \%$ 
B)  $77 \%$ 
C)  $23 \%$ 
D)  $18.7 \%$

Question 11

Solve using the multiplication principle.
-$6 a=-36$

Accepted Answer

A)  1 
B)  -6 
C)  -42 
D)  42 
A)  1 
B)  -6 
C)  -42 
D)  42

Question 12

Determine whether the given number is a solution of the inequality.
-$x \geq 15,9.42$

Accepted Answer

A) True 
 B)False

Question 13

Provide an appropriate response.
-What value of $K$ makes this equation equivalent to $x=4$ ?
$6 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+5$

Accepted Answer

The answer of Provide an appropriate response.
-What value of $K$...

Question 14

Solve the problem.
-During one year, the Cheung's real estate bill included $\$ 345$ for county services. Of this amount, $\$$ 78 went to the highway department. What percent did the county highway department receive? (Round answer to two decimal places.)

Accepted Answer

A)  $22.32 \%$ 
B)  $7.80 \%$ 
C)  $22.61 \%$ 
D)  $77.39 \%$ 
A)  $22.32 \%$ 
B)  $7.80 \%$ 
C)  $22.61 \%$ 
D)  $77.39 \%$

Question 15

Evaluate the formula for the given values of the variables.
-$P=2 L+2 W ; L=3$ in., $W=3$ in.

Accepted Answer

A)  $\mathrm{P}=18$ in. 
B)  $\mathrm{P}=36$ in. 
C)  $\mathrm{P}=12$ in. 
D)  $P=6$ in. 
A)  $\mathrm{P}=18$ in. 
B)  $\mathrm{P}=36$ in. 
C)  $\mathrm{P}=12$ in. 
D)  $P=6$ in.

Question 16

Solve.
-$4 y+24=8 y$

Accepted Answer

A)  -2 
B)  6 
C)  -6 
D)  2 
A)  -2 
B)  6 
C)  -6 
D)  2

Question 17

Solve.
-$8-9 x=5 x-8 x-22$

Accepted Answer

A)  $\frac{11}{3}$ 
B)  $\frac{7}{6}$ 
C)  5 
D)  $\frac{11}{6}$ 
A)  $\frac{11}{3}$ 
B)  $\frac{7}{6}$ 
C)  5 
D)  $\frac{11}{6}$

Question 18

Solve the problem.
-Company A rents copiers for a monthly charge of $\$ 180$ plus 6 cents per copy. Company B rents copiers for a monthly charge of $\$ 360$ plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

Accepted Answer

A)  3000 copies 
B)  6100 copies 
C)  6000 copies 
D)  12,000 copies 
A)  3000 copies 
B)  6100 copies 
C)  6000 copies 
D)  12,000 copies

Question 19

Solve using the addition and multiplication principles.
-$12 y-5 \geq 11 y-2$

Accepted Answer

A)  $\{y \mid y12\}$ 
C)  $\{y \mid y \leq 3\}$ 
D)  $\{y \mid y \geq 3\}$ 
A)  $\{y \mid y12\}$ 
C)  $\{y \mid y \leq 3\}$ 
D)  $\{y \mid y \geq 3\}$

Question 20

Solve the problem. Round to the nearest hundredth, if necessary.
-What is $5 \%$ of 400 ?

Accepted Answer

A)  200 
B)  0.2 
C)  2 
D)  20 
A)  200 
B)  0.2 
C)  2 
D)  20

Solve using the multiplication principle. - $\frac{4}{7}>-2 x$

Solve using the addition and multiplication principles. - $11 a+2 \geq 12 a+12$

Solve. Clear fractions first. - $\frac{1}{5} r+\frac{6}{5}=\frac{1}{7} r+\frac{8}{7}$

Solve using the multiplication principle. - $\frac{5}{7} \mathrm{k}=10$

Solve the problem. -If three times the smaller of two consecutive integers is added to four times the larger, the result is 88. Find the smaller integer.

Solve using the multiplication principle. - $\frac{1}{9} x=22$

Solve the problem. Round to the nearest hundredth, if necessary. - $35 \%$ of what number is 75 ?

Solve. - $4[3-3(x+1)]+1=2(-51-x)+2 x+51$

Solve the equation using the addition principle. - $m+2 \frac{2}{3}=3 \frac{2}{3}$

Solve the problem. -Sales of frozen pizza for a club fund-raiser increased from 500 one year to 615 the next year. What was the percent of increase?

Solve using the multiplication principle. - $6 a=-36$

Determine whether the given number is a solution of the inequality. - $x \geq 15,9.42$

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=4$ ? $6 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+5$

Solve the problem. -During one year, the Cheung's real estate bill included $\$ 345$ for county services. Of this amount, $\$$ 78 went to the highway department. What percent did the county highway department receive? (Round answer to two decimal places.)

Evaluate the formula for the given values of the variables. - $P=2 L+2 W ; L=3$ in., $W=3$ in.

Solve. - $4 y+24=8 y$

Solve. - $8-9 x=5 x-8 x-22$

Solve the problem. -Company A rents copiers for a monthly charge of $\$ 180$ plus 6 cents per copy. Company B rents copiers for a monthly charge of $\$ 360$ plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

Solve using the addition and multiplication principles. - $12 y-5 \geq 11 y-2$

Solve the problem. Round to the nearest hundredth, if necessary. -What is $5 \%$ of 400 ?

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

Introduction to Real Numbers and Algebraic Expressions

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Converting Units of Measurement

Filters

Exam 8: Solving Equations and Inequalities

Solve using the multiplication principle. - 47>−2x\frac{4}{7}>-2 x74​>−2x

Solve using the addition and multiplication principles. - 11a+2≥12a+1211 a+2 \geq 12 a+1211a+2≥12a+12

Solve. Clear fractions first. - 15r+65=17r+87\frac{1}{5} r+\frac{6}{5}=\frac{1}{7} r+\frac{8}{7}51​r+56​=71​r+78​

Solve using the multiplication principle. - 57k=10\frac{5}{7} \mathrm{k}=1075​k=10