8.3 Solve Equations with Variables and Constants on Both Sides

Before you get started, take this readiness quiz.

Simplify: $4 y - 9 + 9 .$
If you missed this problem, review the reference.

Solve: $y + 12 = 16 .$
If you missed this problem, review the reference.

Solve: $−3 y = 63 .$
If you missed this problem, review the reference.

Solve: $3 x + 4 = −8 .$

Solve: $5 a + 3 = −37 .$

Solve: $5 y - 9 = 16 .$

Solve: $3 m - 8 = 19 .$

Solve: $6 n = 5 n + 10 .$

Solve: $−6 c = −7 c + 1 .$

Solve: $3 p - 14 = 5 p .$

Solve: $8 m + 9 = 5 m .$

Solve: $12 j = −4 j + 32 .$

Solve: $8 h = −4 h + 12 .$

Solve: $12 x + 8 = 6 x + 2 .$

Solve: $9 y + 4 = 7 y + 12 .$

Solve: $8 q - 5 = −4 q + 7 .$

Solve: $7 n - 3 = n + 3 .$

Solve: $2 a - 2 = 6 a + 18 .$

Solve: $4 k - 1 = 7 k + 17 .$

Solve: $\frac{7}{8} x - 12 = - \frac{1}{8} x - 2 .$

Solve: $\frac{7}{6} y + 11 = \frac{1}{6} y + 8 .$

Solve: $2.8 x + 12 = −1.4 x - 9 .$

Solve: $3.6 y + 8 = 1.2 y - 4 .$

Solve: $5 \left(x + 3\right) = 35 .$

Solve: $6 \left(y - 4\right) = −18 .$

Solve: $- \left(y + 8\right) = −2 .$

Solve: $- \left(z + 4\right) = −12 .$

Solve: $2 \left(a - 4\right) + 3 = −1 .$

Solve: $7 \left(n - 3\right) - 8 = −15 .$

Solve: $12 - 3 \left(4 j + 3\right) = −17 .$

Solve: $−6 - 8 \left(k - 2\right) = −10 .$

Solve: $6 \left(p - 3\right) - 7 = 5 \left(4 p + 3\right) - 12 .$

Solve: $8 \left(q + 1\right) - 5 = 3 \left(2 q - 4\right) - 1 .$

Solve: $\frac{1}{3} \left(6 u + 3\right) = 7 - u .$

Solve: $\frac{2}{3} \left(9 x - 12\right) = 8 + 2 x .$

Solve: $0.55 \left(100 n + 8\right) = 0.6 \left(85 n + 14\right) .$

Solve: $0.15 \left(40 m - 120\right) = 0.5 \left(60 m + 12\right) .$

Solve the equation for the variable.

$7 x - 8 = 34$

Solve the equation for the variable.

$14 y + 7 = 91$

Solve the equation for the variable.

$4 m + 9 = −23$

Solve the equation for the variable.

$−47 = 6 b + 1$

Solve the equation for the variable.

$29 = −8 x - 3$

Solve the equation for the variable.

$−14 \text{q} - 15 = 13$

Solve the equation for the variable.

$9 k = 8 k - 11$

Solve the equation for the variable.

$6 x + 27 = 9 x$

Solve the equation for the variable.

$b = −4 b - 15$

Solve the equation for the variable.

$7 z = 39 - 6 z$

Solve the equation for the variable.

$8 x + \frac{3}{4} = 7 x$

Solve the equation for the variable.

$−15 r - 8 = −11 r$

Solve the equations for the variable.

$4 x - 17 = 3 x + 2$

Solve the equations for the variable.

$21 + 6 f = 7 f + 14$

Solve the equations for the variable.

$8 q - 5 = 5 q - 20$

Solve the equations for the variable.

$9 c + 7 = −2 c - 37$

Solve the equations for the variable.

$12 x - 17 = −3 x + 13$

Solve the equations for the variable.

$3 y - 4 = 12 - y$

Solve the equations for the variable.

$\frac{4}{3} m - 7 = \frac{1}{3} m - 13$

Solve the equations for the variable.

$11 - \frac{1}{4} a = \frac{3}{4} a + 4$

Solve the equations for the variable.

$\frac{5}{4} a + 15 = \frac{3}{4} a - 5$

Solve the equations for the variable.

$\frac{3}{5} p + 2 = \frac{4}{5} p - 1$

Solve the equations for the variable.

$13 z + 6.45 = 8 z + 23.75$

Solve the equations for the variable.

$2.7 w - 80 = 1.2 w + 10$

Solve the equations for the variable.

$6.6 x - 18.9 = 3.4 x + 54.7$

Solve the linear equation using the general strategy.

$4 \left(y + 7\right) = 64$

Solve the linear equation using the general strategy.

$9 = 3 \left(x - 3\right)$

Solve the linear equation using the general strategy.

$14 \left(y - 6\right) = −42$

Solve the linear equation using the general strategy.

$−7 \left(3 n + 4\right) = 14$

Solve the linear equation using the general strategy.

$8 \left(3 + 3 \text{p}\right) = 0$

Solve the linear equation using the general strategy.

$\frac{3}{5} \left(10 x - 5\right) = 27$

Solve the linear equation using the general strategy.

$4 \left(2.5 v - 0.6\right) = 7.6$

Solve the linear equation using the general strategy.

$0.5 \left(16 m + 34\right) = −15$

Solve the linear equation using the general strategy.

$- \left(t - 8\right) = 17$

Solve the linear equation using the general strategy.

$8 \left(6 b - 7\right) + 23 = 63$

Solve the linear equation using the general strategy.

$13 + 2 \left(m - 4\right) = 17$

Solve the linear equation using the general strategy.

$−9 + 6 \left(5 - k\right) = 12$

Solve the linear equation using the general strategy.

$18 - \left(9 r + 7\right) = −16$

Solve the linear equation using the general strategy.

$18 - 2 \left(y - 3\right) = 32$

Solve the linear equation using the general strategy.

$3 \left(4 n - 1\right) - 2 = 8 n + 3$

Solve the linear equation using the general strategy.

$5 \left(x - 4\right) - 4 x = 14$

Solve the linear equation using the general strategy.

$5 + 6 \left(3 s - 5\right) = −3 + 2 \left(8 s - 1\right)$

Solve the linear equation using the general strategy.

$4 \left(x - 1\right) - 8 = 6 \left(3 x - 2\right) - 7$

Making a fence Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is $150$ feet. The length is $15$ feet more than the width. Find the width, $w ,$ by solving the equation $150 = 2 \left(w + 15\right) + 2 w .$

Coins Rhonda has $\$\text{1}.\text{90}$ in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, $n ,$ by solving the equation $0.05 n + 0.10 \left(2 n - 1\right) = 1.90 .$

When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?

What is the first step you take when solving the equation $3 - 7 \left(y - 4\right) = 38 ?$ Explain why this is your first step.

Using your own words, list the steps in the General Strategy for Solving Linear Equations.