Pre-Algebra Examples

$- 2 < 5 (x + 1) + 2 < 12$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 < 5 x + 5 \cdot 1 + 2 < 12$

Step 1.2

Multiply $5$ by $1$ .

$- 2 < 5 x + 5 + 2 < 12$

Step 2

Add $5$ and $2$ .

$- 2 < 5 x + 7 < 12$

Step 3

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

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Step 3.1

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 - 7 < 5 x < 12 - 7$

Step 3.2

Subtract $7$ from $- 2$ .

$- 9 < 5 x < 12 - 7$

Step 3.3

Subtract $7$ from $12$ .

$- 9 < 5 x < 5$

Step 4

Divide each term in the inequality by $5$ .

$\frac{- 9}{5} < \frac{5 x}{5} < \frac{5}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{9}{5} < \frac{5 x}{5} < \frac{5}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

$- \frac{9}{5} < \frac{5 x}{5} < \frac{5}{5}$

Step 6.2

Divide $x$ by $1$ .

$- \frac{9}{5} < x < \frac{5}{5}$

Step 7

Divide $5$ by $5$ .

$- \frac{9}{5} < x < 1$

Step 8