Solve for x 1/2x-5=10-3/4x

$\frac{1}{2} x - 5 = 10 - \frac{3}{4} x$

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

$\frac{x}{2} - 5 = 10 - \frac{3}{4} x$

Simplify each term.

Combine $x$ and $\frac{3}{4}$ .

$\frac{x}{2} - 5 = 10 - \frac{x \cdot 3}{4}$

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

$\frac{x}{2} - 5 = 10 - \frac{3 x}{4}$

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

Add $\frac{3 x}{4}$ to both sides of the equation.

$\frac{x}{2} - 5 + \frac{3 x}{4} = 10$

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

$\frac{x}{2} \cdot \frac{2}{2} + \frac{3 x}{4} - 5 = 10$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x \cdot 2}{2 \cdot 2} + \frac{3 x}{4} - 5 = 10$

Multiply $2$ by $2$ .

$\frac{x \cdot 2}{4} + \frac{3 x}{4} - 5 = 10$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{4} - 5 = 10$

Add $x \cdot 2$ and $3 x$ .

Reorder $x$ and $2$ .

$\frac{2 \cdot x + 3 x}{4} - 5 = 10$

Add $2 \cdot x$ and $3 x$ .

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

$\frac{5 x}{4} - 5 = 10$

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

Add $5$ to both sides of the equation.

$\frac{5 x}{4} = 10 + 5$

Add $10$ and $5$ .

$\frac{5 x}{4} = 15$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 15$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 15$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot 15$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{4}{5} \cdot 15$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot 15$

Rewrite the expression.

$x = \frac{4}{5} \cdot 15$

Simplify the right side.

Simplify $\frac{4}{5} \cdot 15$ .

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 4 \cdot 3$

Multiply $4$ by $3$ .

$x = 12$

Solve for x 1/2x-5=10-3/4x

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