Solve for x 5(1/2x+2)=4(x-2)

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

Simplify $5 (\frac{1}{2} x + 2)$ .

Start simplifying.

$0 + 0 + 5 (\frac{1}{2} x + 2) = 4 (x - 2)$

Simplify by adding zeros.

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

Combine $\frac{1}{2}$ and $x$ .

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

Apply the distributive property.

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

Combine $5$ and $\frac{x}{2}$ .

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

Multiply $5$ by $2$ .

$\frac{5 x}{2} + 10 = 4 (x - 2)$

Simplify $4 (x - 2)$ .

Apply the distributive property.

$\frac{5 x}{2} + 10 = 4 x + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$\frac{5 x}{2} + 10 = 4 x - 8$

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

Subtract $4 x$ from both sides of the equation.

$\frac{5 x}{2} + 10 - 4 x = - 8$

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2} - 4 x \cdot \frac{2}{2} + 10 = - 8$

Combine $- 4 x$ and $\frac{2}{2}$ .

$\frac{5 x}{2} + \frac{- 4 x \cdot 2}{2} + 10 = - 8$

Combine the numerators over the common denominator.

$\frac{5 x - 4 x \cdot 2}{2} + 10 = - 8$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 4 x \cdot 2$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 4 x \cdot 2}{2} + 10 = - 8$

Factor $x$ out of $- 4 x \cdot 2$ .

$\frac{x \cdot 5 + x (- 4 \cdot 2)}{2} + 10 = - 8$

Factor $x$ out of $x \cdot 5 + x (- 4 \cdot 2)$ .

$\frac{x (5 - 4 \cdot 2)}{2} + 10 = - 8$

Multiply $- 4$ by $2$ .

$\frac{x (5 - 8)}{2} + 10 = - 8$

Subtract $8$ from $5$ .

$\frac{x \cdot - 3}{2} + 10 = - 8$

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{2} + 10 = - 8$

Move the negative in front of the fraction.

$- \frac{3 x}{2} + 10 = - 8$

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

Subtract $10$ from both sides of the equation.

$- \frac{3 x}{2} = - 8 - 10$

Subtract $10$ from $- 8$ .

$- \frac{3 x}{2} = - 18$

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 18$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 18$

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot - 18$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 18$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 18$

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot - 18$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot - 18$

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot - 18$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot - 18$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x = \frac{- 2}{3} \cdot - 18$

Factor $3$ out of $- 18$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot - 6$

Multiply $- 2$ by $- 6$ .

$x = 12$

Solve for x 5(1/2x+2)=4(x-2)

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