Solve for a a+3/4a=21

$a + \frac{3}{4} a = 21$

Step 1

Simplify $a + \frac{3}{4} a$ .

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

$a + \frac{3 a}{4} = 21$

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

$a \cdot \frac{4}{4} + \frac{3 a}{4} = 21$

Simplify terms.

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

$\frac{a \cdot 4}{4} + \frac{3 a}{4} = 21$

Combine the numerators over the common denominator.

$\frac{a \cdot 4 + 3 a}{4} = 21$

Simplify the numerator.

Move $4$ to the left of $a$ .

$\frac{4 \cdot a + 3 a}{4} = 21$

Add $4 a$ and $3 a$ .

$\frac{7 a}{4} = 21$

Step 2

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 a}{4} = \frac{4}{7} \cdot 21$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{7} \cdot \frac{7 a}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 a}{4} = \frac{4}{7} \cdot 21$

Rewrite the expression.

$\frac{1}{7} (7 a) = \frac{4}{7} \cdot 21$

Cancel the common factor of $7$ .

Factor $7$ out of $7 a$ .

$\frac{1}{7} (7 (a)) = \frac{4}{7} \cdot 21$

Cancel the common factor.

$\frac{1}{7} (7 a) = \frac{4}{7} \cdot 21$

Rewrite the expression.

$a = \frac{4}{7} \cdot 21$

Simplify the right side.

Simplify $\frac{4}{7} \cdot 21$ .

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

$a = \frac{4}{7} \cdot (7 (3))$

Cancel the common factor.

$a = \frac{4}{7} \cdot (7 \cdot 3)$

Rewrite the expression.

$a = 4 \cdot 3$

Multiply $4$ by $3$ .

$a = 12$

Solve for a a+3/4a=21

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