Algebra Examples

$- 12 < \frac{1}{2} (4 x + 16) < 18$

Step 1

Apply the distributive property.

$- 12 < \frac{1}{2} \cdot (4 x) + \frac{1}{2} \cdot 16 < 18$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4 x$ .

$- 12 < \frac{1}{2} \cdot (2 (2 x)) + \frac{1}{2} \cdot 16 < 18$

Step 2.2

Cancel the common factor.

$- 12 < \frac{1}{2} \cdot (2 (2 x)) + \frac{1}{2} \cdot 16 < 18$

Step 2.3

Rewrite the expression.

$- 12 < 2 x + \frac{1}{2} \cdot 16 < 18$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $16$ .

$- 12 < 2 x + \frac{1}{2} \cdot (2 (8)) < 18$

Step 3.2

Cancel the common factor.

$- 12 < 2 x + \frac{1}{2} \cdot (2 \cdot 8) < 18$

Step 3.3

Rewrite the expression.

$- 12 < 2 x + 8 < 18$

Step 4

Move all terms not containing $x$ from the center section of the inequality.

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Step 4.1

Subtract $8$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 - 8 < 2 x < 18 - 8$

Step 4.2

Subtract $8$ from $- 12$ .

$- 20 < 2 x < 18 - 8$

Step 4.3

Subtract $8$ from $18$ .

$- 20 < 2 x < 10$

Step 5

Divide each term in the inequality by $2$ .

$\frac{- 20}{2} < \frac{2 x}{2} < \frac{10}{2}$

Step 6

Divide $- 20$ by $2$ .

$- 10 < \frac{2 x}{2} < \frac{10}{2}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

$- 10 < \frac{2 x}{2} < \frac{10}{2}$

Step 7.2

Divide $x$ by $1$ .

$- 10 < x < \frac{10}{2}$

Step 8

Divide $10$ by $2$ .

$- 10 < x < 5$

Step 9