Solve for x 3/4x-1/2=7

$\frac{3}{4} x - \frac{1}{2} = 7$

Step 1

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

$\frac{3 x}{4} - \frac{1}{2} = 7$

Step 2

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

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{3 x}{4} = 7 + \frac{1}{2}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} = 7 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $7$ and $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{7 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{7 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{3 x}{4} = \frac{14 + 1}{2}$

Add $14$ and $1$ .

$\frac{3 x}{4} = \frac{15}{2}$

Step 3

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{15}{2}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{15}{2}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{15}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot \frac{15}{2}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{15}{2}$

Rewrite the expression.

$x = \frac{4}{3} \cdot \frac{15}{2}$

Simplify the right side.

Simplify $\frac{4}{3} \cdot \frac{15}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{3} \cdot \frac{15}{2}$

Cancel the common factor.

$x = \frac{2 \cdot 2}{3} \cdot \frac{15}{2}$

Rewrite the expression.

$x = \frac{2}{3} \cdot 15$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 2 \cdot 5$

Multiply $2$ by $5$ .

$x = 10$

Solve for x 3/4x-1/2=7

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