Solve for x x/2=(3x)/4+5

$\frac{x}{2} = \frac{3 x}{4} + 5$

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $(\frac{3 x}{4} + 5) \cdot 2$ .

Apply the distributive property.

$x = \frac{3 x}{4} \cdot 2 + 5 \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

$x = \frac{3 x}{2 \cdot 2} \cdot 2 + 5 \cdot 2$

Rewrite the expression.

$x = \frac{3 x}{2} + 5 \cdot 2$

Multiply $5$ by $2$ .

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

Step 3

Solve for $x$ .

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

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $2$ to the left of $x$ .

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

Subtract $3 x$ from $2 x$ .

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

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot 10$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

$- 2 \frac{- x}{2} = - 2 \cdot 10$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot 10$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 \cdot 10$

Rewrite the expression.

$- - x = - 2 \cdot 10$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 10$

Multiply $x$ by $1$ .

$x = - 2 \cdot 10$

Simplify the right side.

Multiply $- 2$ by $10$ .

$x = - 20$

Solve for x x/2=(3x)/4+5

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