Solve the Absolute Value Inequality for a |2a-10|=6

$| 2 a - 10 | = 6$

Step 1

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

$2 a - 10 = \pm 6$

Step 2

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

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

$2 a - 10 = 6$

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

Add $10$ to both sides of the equation.

$2 a = 6 + 10$

Add $6$ and $10$ .

$2 a = 16$

Divide each term in $2 a = 16$ by $2$ and simplify.

Divide each term in $2 a = 16$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Divide $16$ by $2$ .

$a = 8$

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

$2 a - 10 = - 6$

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

Add $10$ to both sides of the equation.

$2 a = - 6 + 10$

Add $- 6$ and $10$ .

$2 a = 4$

Divide each term in $2 a = 4$ by $2$ and simplify.

Divide each term in $2 a = 4$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Divide $4$ by $2$ .

$a = 2$

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

$a = 8, 2$

Solve the Absolute Value Inequality for a |2a-10|=6

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