Solve for x 3/4(2x-16)=1/3(x+6)

$\frac{3}{4} (2 x - 16) = \frac{1}{3} (x + 6)$

Step 1

Simplify $\frac{3}{4} \cdot (2 x - 16)$ .

Rewrite.

$0 + 0 + \frac{3}{4} \cdot (2 x - 16) = \frac{1}{3} \cdot (x + 6)$

Simplify by adding zeros.

$\frac{3}{4} \cdot (2 x - 16) = \frac{1}{3} \cdot (x + 6)$

Apply the distributive property.

$\frac{3}{4} (2 x) + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} (2 x) + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Factor $2$ out of $2 x$ .

$\frac{3}{2 (2)} (2 (x)) + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Cancel the common factor.

$\frac{3}{2 \cdot 2} (2 x) + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Rewrite the expression.

$\frac{3}{2} x + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + \frac{3}{4} \cdot - 16 = \frac{1}{3} \cdot (x + 6)$

Cancel the common factor of $4$ .

Factor $4$ out of $- 16$ .

$\frac{3 x}{2} + \frac{3}{4} \cdot (4 (- 4)) = \frac{1}{3} \cdot (x + 6)$

Cancel the common factor.

$\frac{3 x}{2} + \frac{3}{4} \cdot (4 \cdot - 4) = \frac{1}{3} \cdot (x + 6)$

Rewrite the expression.

$\frac{3 x}{2} + 3 \cdot - 4 = \frac{1}{3} \cdot (x + 6)$

Multiply $3$ by $- 4$ .

$\frac{3 x}{2} - 12 = \frac{1}{3} \cdot (x + 6)$

Step 2

Simplify $\frac{1}{3} \cdot (x + 6)$ .

Apply the distributive property.

$\frac{3 x}{2} - 12 = \frac{1}{3} x + \frac{1}{3} \cdot 6$

Combine $\frac{1}{3}$ and $x$ .

$\frac{3 x}{2} - 12 = \frac{x}{3} + \frac{1}{3} \cdot 6$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{3 x}{2} - 12 = \frac{x}{3} + \frac{1}{3} \cdot (3 (2))$

Cancel the common factor.

$\frac{3 x}{2} - 12 = \frac{x}{3} + \frac{1}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$\frac{3 x}{2} - 12 = \frac{x}{3} + 2$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{x}{3}$ from both sides of the equation.

$\frac{3 x}{2} - 12 - \frac{x}{3} = 2$

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{2} \cdot \frac{3}{3} - \frac{x}{3} - 12 = 2$

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{2}{2} - 12 = 2$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{2}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{2 \cdot 3} - \frac{x}{3} \cdot \frac{2}{2} - 12 = 2$

Multiply $2$ by $3$ .

$\frac{3 x \cdot 3}{6} - \frac{x}{3} \cdot \frac{2}{2} - 12 = 2$

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 3}{6} - \frac{x \cdot 2}{3 \cdot 2} - 12 = 2$

Multiply $3$ by $2$ .

$\frac{3 x \cdot 3}{6} - \frac{x \cdot 2}{6} - 12 = 2$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - x \cdot 2}{6} - 12 = 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 - x \cdot 2$ .

Factor $x$ out of $3 x \cdot 3$ .

$\frac{x (3 \cdot 3) - x \cdot 2}{6} - 12 = 2$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x (3 \cdot 3) + x (- 1 \cdot 2)}{6} - 12 = 2$

Factor $x$ out of $x (3 \cdot 3) + x (- 1 \cdot 2)$ .

$\frac{x (3 \cdot 3 - 1 \cdot 2)}{6} - 12 = 2$

Multiply $3$ by $3$ .

$\frac{x (9 - 1 \cdot 2)}{6} - 12 = 2$

Multiply $- 1$ by $2$ .

$\frac{x (9 - 2)}{6} - 12 = 2$

Subtract $2$ from $9$ .

$\frac{x \cdot 7}{6} - 12 = 2$

Move $7$ to the left of $x$ .

$\frac{7 x}{6} - 12 = 2$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $12$ to both sides of the equation.

$\frac{7 x}{6} = 2 + 12$

Add $2$ and $12$ .

$\frac{7 x}{6} = 14$

Step 5

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot 14$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{7} \cdot \frac{7 x}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot 14$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 14$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{6}{7} \cdot 14$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 14$

Rewrite the expression.

$x = \frac{6}{7} \cdot 14$

Simplify the right side.

Simplify $\frac{6}{7} \cdot 14$ .

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$x = \frac{6}{7} \cdot (7 (2))$

Cancel the common factor.

$x = \frac{6}{7} \cdot (7 \cdot 2)$

Rewrite the expression.

$x = 6 \cdot 2$

Multiply $6$ by $2$ .

$x = 12$

Solve for x 3/4(2x-16)=1/3(x+6)

Related Questions

Support LCMGCF.com by disabling your adblocker.