Basic Math Examples

$\frac{1}{3} \cdot (6 a - 12) = 4 (\frac{1}{2} a + 1) - 2$

Step 1

Simplify $\frac{1}{3} \cdot (6 a - 12)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (6 a - 12) = 4 (\frac{1}{2} a + 1) - 2$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (6 a - 12) = 4 (\frac{1}{2} a + 1) - 2$

Step 1.3

Apply the distributive property.

$\frac{1}{3} (6 a) + \frac{1}{3} \cdot - 12 = 4 (\frac{1}{2} a + 1) - 2$

Step 1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.4.1

Factor $3$ out of $6 a$ .

$\frac{1}{3} (3 (2 a)) + \frac{1}{3} \cdot - 12 = 4 (\frac{1}{2} a + 1) - 2$

Step 1.4.2

Cancel the common factor.

$\frac{1}{3} (3 (2 a)) + \frac{1}{3} \cdot - 12 = 4 (\frac{1}{2} a + 1) - 2$

Step 1.4.3

Rewrite the expression.

$2 a + \frac{1}{3} \cdot - 12 = 4 (\frac{1}{2} a + 1) - 2$

Step 1.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.1

Factor $3$ out of $- 12$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

Simplify $4 (\frac{1}{2} a + 1) - 2$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine $\frac{1}{2}$ and $a$ .

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.3.1

Factor $2$ out of $4$ .

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

Step 2.1.3.2

Cancel the common factor.

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

Step 2.1.3.3

Rewrite the expression.

$2 a - 4 = 2 a + 4 \cdot 1 - 2$

Step 2.1.4

Multiply $4$ by $1$ .

$2 a - 4 = 2 a + 4 - 2$

Step 2.2

Subtract $2$ from $4$ .

$2 a - 4 = 2 a + 2$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $2 a$ from both sides of the equation.

$2 a - 4 - 2 a = 2$

Step 3.2

Combine the opposite terms in $2 a - 4 - 2 a$ .

Tap for more steps...

Step 3.2.1

Subtract $2 a$ from $2 a$ .

$0 - 4 = 2$

Step 3.2.2

Subtract $4$ from $0$ .

$- 4 = 2$

Step 4

Since $- 4 \neq 2$ , there are no solutions.

No solution