8.2 Solve Equations Using the Division and Multiplication Properties of Equality

Before you get started, take this readiness quiz.

Simplify: $−7 \left(\frac{1}{−7}\right) .$
If you missed this problem, review the reference.

What is the reciprocal of $- \frac{3}{8} ?$
If you missed this problem, review the reference.

Evaluate $9 x + 2$ when $x = −3 .$
If you missed this problem, review the reference.

Solve: $3 y = −48 .$

Solve: $4 z = −52 .$

Solve: $\frac{ b}{−6} = −24 .$

Solve: $\frac{ c}{−8} = −16 .$

Solve: $- k = 8 .$

Solve: $- g = 3 .$

Solve: $\frac{2}{5} n = 14 .$

Solve: $\frac{5}{6} y = 15 .$

Solve: $7 x + 6 x - 4 x = −8 + 26 .$

Solve: $11 n - 3 n - 6 n = 7 - 17 .$

Solve: $18 - 27 = 15 c - 9 c - 3 c .$

Solve: $18 - 22 = 12 x - x - 4 x .$

Solve: $−4 \left(n - 2\right) - 8 = 24 .$

Solve: $−6 \left(n - 2\right) - 12 = 30 .$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$7 p = 63$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$−9 x = −27$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$−72 = 12 y$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$−8 m = −56$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$0.75 a = 11.25$

Solve each equation for the variable using the Division Property of Equality and check the solution.

$4 x = 0$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{z}{2} = 14$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{ c}{−3} = −12$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{q}{6} = −8$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$−4 = \frac{p}{−20}$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{3}{5} r = 15$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$24 = - \frac{3}{4} x$

Solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$- \frac{1}{3} q = - \frac{5}{6}$

Solve the equation.

$6 y - 3 y + 12 y = −43 + 28$

Solve the equation.

$−5 m + 7 m - 8 m = −6 + 36$

Solve the equation.

$−18 - 7 = 5 t - 9 t - 6 t$

Solve the equation.

$\frac{5}{12} q + \frac{1}{2} q = 25 - 3$

Solve the equation.

$0.05 p - 0.01 p = 2 + 0.24$

Teaching Connie’s kindergarten class has $24$ children. She wants them to get into $4$ equal groups. Find the number of children in each group, $g ,$ by solving the equation $4 g = 24 .$

Unit price Nishant paid $\$\text{12}.\text{96}$ for a pack of $12$ juice bottles. Find the price of each bottle, $b ,$ by solving the equation $12 b = 12.96 .$

Fabric The drill team used $14$ yards of fabric to make flags for one-third of the members. Find how much fabric, $f ,$ they would need to make flags for the whole team by solving the equation $\frac{1}{3} f = 14 .$

Emiliano thinks $x = 40$ is the solution to the equation $\frac{1}{2} x = 80 .$ Explain why he is wrong.