Basic Math Examples

$\frac{1}{6} \cdot (a + 2) = 2 a - 2 (4 - a) - 7$

Step 1

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 a - 2 (4 - a) - 7 = \frac{1}{6} \cdot (a + 2)$

Step 2

Simplify $2 a - 2 (4 - a) - 7$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$2 a - 2 \cdot 4 - 2 (- a) - 7 = \frac{1}{6} \cdot (a + 2)$

Step 2.1.2

Multiply $- 2$ by $4$ .

$2 a - 8 - 2 (- a) - 7 = \frac{1}{6} \cdot (a + 2)$

Step 2.1.3

Multiply $- 1$ by $- 2$ .

$2 a - 8 + 2 a - 7 = \frac{1}{6} \cdot (a + 2)$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Add $2 a$ and $2 a$ .

$4 a - 8 - 7 = \frac{1}{6} \cdot (a + 2)$

Step 2.2.2

Subtract $7$ from $- 8$ .

$4 a - 15 = \frac{1}{6} \cdot (a + 2)$

Step 3

Simplify $\frac{1}{6} \cdot (a + 2)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$4 a - 15 = \frac{1}{6} a + \frac{1}{6} \cdot 2$

Step 3.2

Combine $\frac{1}{6}$ and $a$ .

$4 a - 15 = \frac{a}{6} + \frac{1}{6} \cdot 2$

Step 3.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.1

Factor $2$ out of $6$ .

$4 a - 15 = \frac{a}{6} + \frac{1}{2 (3)} \cdot 2$

Step 3.3.2

Cancel the common factor.

$4 a - 15 = \frac{a}{6} + \frac{1}{2 \cdot 3} \cdot 2$

Step 3.3.3

Rewrite the expression.

$4 a - 15 = \frac{a}{6} + \frac{1}{3}$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $\frac{a}{6}$ from both sides of the equation.

$4 a - 15 - \frac{a}{6} = \frac{1}{3}$

Step 4.2

To write $4 a$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$4 a \cdot \frac{6}{6} - \frac{a}{6} - 15 = \frac{1}{3}$

Step 4.3

Combine $4 a$ and $\frac{6}{6}$ .

$\frac{4 a \cdot 6}{6} - \frac{a}{6} - 15 = \frac{1}{3}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{4 a \cdot 6 - a}{6} - 15 = \frac{1}{3}$

Step 4.5

Simplify each term.

Tap for more steps...

Step 4.5.1

Simplify the numerator.

Tap for more steps...

Step 4.5.1.1

Factor $a$ out of $4 a \cdot 6 - a$ .

Tap for more steps...

Step 4.5.1.1.1

Factor $a$ out of $4 a \cdot 6$ .

$\frac{a (4 \cdot 6) - a}{6} - 15 = \frac{1}{3}$

Step 4.5.1.1.2

Factor $a$ out of $- a$ .

$\frac{a (4 \cdot 6) + a \cdot - 1}{6} - 15 = \frac{1}{3}$

Step 4.5.1.1.3

Factor $a$ out of $a (4 \cdot 6) + a \cdot - 1$ .

$\frac{a (4 \cdot 6 - 1)}{6} - 15 = \frac{1}{3}$

Step 4.5.1.2

Multiply $4$ by $6$ .

$\frac{a (24 - 1)}{6} - 15 = \frac{1}{3}$

Step 4.5.1.3

Subtract $1$ from $24$ .

$\frac{a \cdot 23}{6} - 15 = \frac{1}{3}$

Step 4.5.2

Move $23$ to the left of $a$ .

$\frac{23 a}{6} - 15 = \frac{1}{3}$

Step 5

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

Tap for more steps...

Step 5.1

Add $15$ to both sides of the equation.

$\frac{23 a}{6} = \frac{1}{3} + 15$

Step 5.2

To write $15$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{23 a}{6} = \frac{1}{3} + 15 \cdot \frac{3}{3}$

Step 5.3

Combine $15$ and $\frac{3}{3}$ .

$\frac{23 a}{6} = \frac{1}{3} + \frac{15 \cdot 3}{3}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{23 a}{6} = \frac{1 + 15 \cdot 3}{3}$

Step 5.5

Simplify the numerator.

Tap for more steps...

Step 5.5.1

Multiply $15$ by $3$ .

$\frac{23 a}{6} = \frac{1 + 45}{3}$

Step 5.5.2

Add $1$ and $45$ .

$\frac{23 a}{6} = \frac{46}{3}$

Step 6

Multiply both sides of the equation by $\frac{6}{23}$ .

$\frac{6}{23} \cdot \frac{23 a}{6} = \frac{6}{23} \cdot \frac{46}{3}$

Step 7

Simplify both sides of the equation.

Tap for more steps...

Step 7.1

Simplify the left side.

Tap for more steps...

Step 7.1.1

Simplify $\frac{6}{23} \cdot \frac{23 a}{6}$ .

Tap for more steps...

Step 7.1.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 7.1.1.1.1

Cancel the common factor.

$\frac{6}{23} \cdot \frac{23 a}{6} = \frac{6}{23} \cdot \frac{46}{3}$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{23} (23 a) = \frac{6}{23} \cdot \frac{46}{3}$

Step 7.1.1.2

Cancel the common factor of $23$ .

Tap for more steps...

Step 7.1.1.2.1

Factor $23$ out of $23 a$ .

$\frac{1}{23} (23 (a)) = \frac{6}{23} \cdot \frac{46}{3}$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{23} (23 a) = \frac{6}{23} \cdot \frac{46}{3}$

Step 7.1.1.2.3

Rewrite the expression.

$a = \frac{6}{23} \cdot \frac{46}{3}$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Simplify $\frac{6}{23} \cdot \frac{46}{3}$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.2.1.1.1

Factor $3$ out of $6$ .

$a = \frac{3 (2)}{23} \cdot \frac{46}{3}$

Step 7.2.1.1.2

Cancel the common factor.

$a = \frac{3 \cdot 2}{23} \cdot \frac{46}{3}$

Step 7.2.1.1.3

Rewrite the expression.

$a = \frac{2}{23} \cdot 46$

Step 7.2.1.2

Cancel the common factor of $23$ .

Tap for more steps...

Step 7.2.1.2.1

Factor $23$ out of $46$ .

$a = \frac{2}{23} \cdot (23 (2))$

Step 7.2.1.2.2

Cancel the common factor.

$a = \frac{2}{23} \cdot (23 \cdot 2)$

Step 7.2.1.2.3

Rewrite the expression.

$a = 2 \cdot 2$

Step 7.2.1.3

Multiply $2$ by $2$ .

$a = 4$