Pre-Algebra Examples

$| 3 a + 8 | = | 3 a - 6 |$

Step 1

Rewrite the equation as $| 3 a - 6 | = | 3 a + 8 |$ .

$| 3 a - 6 | = | 3 a + 8 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$3 a - 6 = 3 a + 8$

$3 a - 6 = - (3 a + 8)$

$- (3 a - 6) = 3 a + 8$

$- (3 a - 6) = - (3 a + 8)$

Step 3

After simplifying, there are only two unique equations to be solved.

$3 a - 6 = 3 a + 8$

$3 a - 6 = - (3 a + 8)$

Step 4

Solve $3 a - 6 = 3 a + 8$ for $a$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

$3 a - 6 - 3 a = 8$

Step 4.1.2

Combine the opposite terms in $3 a - 6 - 3 a$ .

Tap for more steps...

Step 4.1.2.1

Subtract $3 a$ from $3 a$ .

$0 - 6 = 8$

Step 4.1.2.2

Subtract $6$ from $0$ .

$- 6 = 8$

Step 4.2

Since $- 6 \neq 8$ , there are no solutions.

No solution

Step 5

Solve $3 a - 6 = - (3 a + 8)$ for $a$ .

Tap for more steps...

Step 5.1

Simplify $- (3 a + 8)$ .

Tap for more steps...

Step 5.1.1

Rewrite.

$3 a - 6 = 0 + 0 - (3 a + 8)$

Step 5.1.2

Simplify by adding zeros.

$3 a - 6 = - (3 a + 8)$

Step 5.1.3

Apply the distributive property.

$3 a - 6 = - (3 a) - 1 \cdot 8$

Step 5.1.4

Multiply.

Tap for more steps...

Step 5.1.4.1

Multiply $3$ by $- 1$ .

$3 a - 6 = - 3 a - 1 \cdot 8$

Step 5.1.4.2

Multiply $- 1$ by $8$ .

$3 a - 6 = - 3 a - 8$

Step 5.2

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

Tap for more steps...

Step 5.2.1

Add $3 a$ to both sides of the equation.

$3 a - 6 + 3 a = - 8$

Step 5.2.2

Add $3 a$ and $3 a$ .

$6 a - 6 = - 8$

Step 5.3

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

Tap for more steps...

Step 5.3.1

Add $6$ to both sides of the equation.

$6 a = - 8 + 6$

Step 5.3.2

Add $- 8$ and $6$ .

$6 a = - 2$

Step 5.4

Divide each term in $6 a = - 2$ by $6$ and simplify.

Tap for more steps...

Step 5.4.1

Divide each term in $6 a = - 2$ by $6$ .

$\frac{6 a}{6} = \frac{- 2}{6}$

Step 5.4.2

Simplify the left side.

Tap for more steps...

Step 5.4.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 5.4.2.1.1

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 2}{6}$

Step 5.4.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 2}{6}$

Step 5.4.3

Simplify the right side.

Tap for more steps...

Step 5.4.3.1

Cancel the common factor of $- 2$ and $6$ .

Tap for more steps...

Step 5.4.3.1.1

Factor $2$ out of $- 2$ .

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

Step 5.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 5.4.3.1.2.1

Factor $2$ out of $6$ .

$a = \frac{2 \cdot - 1}{2 \cdot 3}$

Step 5.4.3.1.2.2

Cancel the common factor.

$a = \frac{2 \cdot - 1}{2 \cdot 3}$

Step 5.4.3.1.2.3

Rewrite the expression.

$a = \frac{- 1}{3}$

Step 5.4.3.2

Move the negative in front of the fraction.

$a = - \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{1}{3}$

Decimal Form:

$a = - 0.\overline{3}$