Solve for x -1/2(-10x+6)+x=3/2(6x-4)

$- \frac{1}{2} (- 10 x + 6) + x = \frac{3}{2} (6 x - 4)$

Simplify $- \frac{1}{2} \cdot (- 10 x + 6) + x$ .

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} (- 10 x) - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (- 10 x) - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Factor $2$ out of $- 10 x$ .

$\frac{- 1}{2} (2 (- 5 x)) - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Cancel the common factor.

$\frac{- 1}{2} (2 (- 5 x)) - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Rewrite the expression.

$- 1 (- 5 x) - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Multiply $- 5$ by $- 1$ .

$5 x - \frac{1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$5 x + \frac{- 1}{2} \cdot 6 + x = \frac{3}{2} \cdot (6 x - 4)$

Factor $2$ out of $6$ .

$5 x + \frac{- 1}{2} \cdot (2 (3)) + x = \frac{3}{2} \cdot (6 x - 4)$

Cancel the common factor.

$5 x + \frac{- 1}{2} \cdot (2 \cdot 3) + x = \frac{3}{2} \cdot (6 x - 4)$

Rewrite the expression.

$5 x - 1 \cdot 3 + x = \frac{3}{2} \cdot (6 x - 4)$

Multiply $- 1$ by $3$ .

$5 x - 3 + x = \frac{3}{2} \cdot (6 x - 4)$

Add $5 x$ and $x$ .

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

Simplify $\frac{3}{2} \cdot (6 x - 4)$ .

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $3$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$6 x - 3 = 9 x + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$6 x - 3 = 9 x - 6$

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

Subtract $9 x$ from both sides of the equation.

$6 x - 3 - 9 x = - 6$

Subtract $9 x$ from $6 x$ .

$- 3 x - 3 = - 6$

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

Add $3$ to both sides of the equation.

$- 3 x = - 6 + 3$

Add $- 6$ and $3$ .

$- 3 x = - 3$

Divide each term in $- 3 x = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 3$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x = 1$

Solve for x -1/2(-10x+6)+x=3/2(6x-4)

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