Basic Math Examples

$| \frac{3}{4} a - 7 | = 5$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{3}{4} a - 7 = \pm 5$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$\frac{3}{4} a - 7 = 5$

Step 2.2

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

$\frac{3 a}{4} - 7 = 5$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Add $7$ to both sides of the equation.

$\frac{3 a}{4} = 5 + 7$

Step 2.3.2

Add $5$ and $7$ .

$\frac{3 a}{4} = 12$

Step 2.4

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

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} \cdot 12$

Step 2.5

Simplify both sides of the equation.

Tap for more steps...

Step 2.5.1

Simplify the left side.

Tap for more steps...

Step 2.5.1.1

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

Tap for more steps...

Step 2.5.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.5.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} \cdot 12$

Step 2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 a) = \frac{4}{3} \cdot 12$

Step 2.5.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.5.1.1.2.1

Factor $3$ out of $3 a$ .

$\frac{1}{3} (3 (a)) = \frac{4}{3} \cdot 12$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 a) = \frac{4}{3} \cdot 12$

Step 2.5.1.1.2.3

Rewrite the expression.

$a = \frac{4}{3} \cdot 12$

Step 2.5.2

Simplify the right side.

Tap for more steps...

Step 2.5.2.1

Simplify $\frac{4}{3} \cdot 12$ .

Tap for more steps...

Step 2.5.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.5.2.1.1.1

Factor $3$ out of $12$ .

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

Step 2.5.2.1.1.2

Cancel the common factor.

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

Step 2.5.2.1.1.3

Rewrite the expression.

$a = 4 \cdot 4$

Step 2.5.2.1.2

Multiply $4$ by $4$ .

$a = 16$

Step 2.6

Next, use the negative value of the $\pm$ to find the second solution.

$\frac{3}{4} a - 7 = - 5$

Step 2.7

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

$\frac{3 a}{4} - 7 = - 5$

Step 2.8

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

Tap for more steps...

Step 2.8.1

Add $7$ to both sides of the equation.

$\frac{3 a}{4} = - 5 + 7$

Step 2.8.2

Add $- 5$ and $7$ .

$\frac{3 a}{4} = 2$

Step 2.9

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

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} \cdot 2$

Step 2.10

Simplify both sides of the equation.

Tap for more steps...

Step 2.10.1

Simplify the left side.

Tap for more steps...

Step 2.10.1.1

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

Tap for more steps...

Step 2.10.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.10.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} \cdot 2$

Step 2.10.1.1.1.2

Rewrite the expression.

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

Step 2.10.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.10.1.1.2.1

Factor $3$ out of $3 a$ .

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

Step 2.10.1.1.2.2

Cancel the common factor.

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

Step 2.10.1.1.2.3

Rewrite the expression.

$a = \frac{4}{3} \cdot 2$

Step 2.10.2

Simplify the right side.

Tap for more steps...

Step 2.10.2.1

Multiply $\frac{4}{3} \cdot 2$ .

Tap for more steps...

Step 2.10.2.1.1

Combine $\frac{4}{3}$ and $2$ .

$a = \frac{4 \cdot 2}{3}$

Step 2.10.2.1.2

Multiply $4$ by $2$ .

$a = \frac{8}{3}$

Step 2.11

The complete solution is the result of both the positive and negative portions of the solution.

$a = 16, \frac{8}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = 16, \frac{8}{3}$

Decimal Form:

$a = 16, 2.\overline{6}$

Mixed Number Form:

$a = 16, 2 \frac{2}{3}$