Solve for x 1/4(8x-12)=1/3(9x-6)

$\frac{1}{4} (8 x - 12) = \frac{1}{3} (9 x - 6)$

Step 1

Simplify $\frac{1}{4} \cdot (8 x - 12)$ .

Rewrite.

$0 + 0 + \frac{1}{4} \cdot (8 x - 12) = \frac{1}{3} \cdot (9 x - 6)$

Simplify by adding zeros.

$\frac{1}{4} \cdot (8 x - 12) = \frac{1}{3} \cdot (9 x - 6)$

Apply the distributive property.

$\frac{1}{4} (8 x) + \frac{1}{4} \cdot - 12 = \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor of $4$ .

Factor $4$ out of $8 x$ .

$\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 12 = \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor.

$\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 12 = \frac{1}{3} \cdot (9 x - 6)$

Rewrite the expression.

$2 x + \frac{1}{4} \cdot - 12 = \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor of $4$ .

Factor $4$ out of $- 12$ .

$2 x + \frac{1}{4} \cdot (4 (- 3)) = \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor.

$2 x + \frac{1}{4} \cdot (4 \cdot - 3) = \frac{1}{3} \cdot (9 x - 6)$

Rewrite the expression.

$2 x - 3 = \frac{1}{3} \cdot (9 x - 6)$

Step 2

Simplify $\frac{1}{3} \cdot (9 x - 6)$ .

Apply the distributive property.

$2 x - 3 = \frac{1}{3} (9 x) + \frac{1}{3} \cdot - 6$

Cancel the common factor of $3$ .

Factor $3$ out of $9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x - 3 = 3 x - 2$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$2 x - 3 - 3 x = - 2$

Subtract $3 x$ from $2 x$ .

$- x - 3 = - 2$

Step 4

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

Add $3$ to both sides of the equation.

$- x = - 2 + 3$

Add $- 2$ and $3$ .

$- x = 1$

Step 5

Divide each term in $- x = 1$ by $- 1$ and simplify.

Divide each term in $- x = 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{1}{- 1}$

Divide $x$ by $1$ .

$x = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$x = - 1$

Solve for x 1/4(8x-12)=1/3(9x-6)

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