Basic Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.2.1

Factor $2$ out of $6$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.3.1

Factor $2$ out of $- 2 a$ .

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

Step 1.1.3.2

Cancel the common factor.

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

Step 1.1.3.3

Rewrite the expression.

$3 - a + 6 a = 3 a$

Step 1.2

Add $- a$ and $6 a$ .

$3 + 5 a = 3 a$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $3 a$ from both sides of the equation.

$3 + 5 a - 3 a = 0$

Step 2.2

Subtract $3 a$ from $5 a$ .

$3 + 2 a = 0$

Step 3

Subtract $3$ from both sides of the equation.

$2 a = - 3$

Step 4

Divide each term in $2 a = - 3$ by $2$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $2 a = - 3$ by $2$ .

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

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $a$ by $1$ .

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

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 1.5$

Mixed Number Form:

$a = - 1 \frac{1}{2}$