Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $4$ by $2$ .

$\frac{3 x}{4} = \frac{8 + 1}{2}$

Step 2.5.2

Add $8$ and $1$ .

$\frac{3 x}{4} = \frac{9}{2}$

Step 3

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

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

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

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

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{9}{2}$

Step 4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot \frac{9}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{9}{2}$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{4}{3} \cdot \frac{9}{2}$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.1

Factor $2$ out of $4$ .

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

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{2 \cdot 2}{3} \cdot \frac{9}{2}$

Step 4.2.1.1.3

Rewrite the expression.

$x = \frac{2}{3} \cdot 9$

Step 4.2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.2.1

Factor $3$ out of $9$ .

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

Step 4.2.1.2.2

Cancel the common factor.

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

Step 4.2.1.2.3

Rewrite the expression.

$x = 2 \cdot 3$

Step 4.2.1.3

Multiply $2$ by $3$ .

$x = 6$