Pre-Algebra Examples

$- 8 < \frac{8 x - 5}{8} < 5$

Step 1

Multiply each term in the inequality by $8$ .

$- 8 \cdot 8 < \frac{8 x - 5}{8} \cdot 8 < 5 \cdot 8$

Step 2

Multiply $- 8$ by $8$ .

$- 64 < \frac{8 x - 5}{8} \cdot 8 < 5 \cdot 8$

Step 3

Cancel the common factor of $8$ .

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Step 3.1

Cancel the common factor.

$- 64 < \frac{8 x - 5}{8} \cdot 8 < 5 \cdot 8$

Step 3.2

Rewrite the expression.

$- 64 < 8 x - 5 < 5 \cdot 8$

Step 4

Multiply $5$ by $8$ .

$- 64 < 8 x - 5 < 40$

Step 5

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

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Step 5.1

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 64 + 5 < 8 x < 40 + 5$

Step 5.2

Add $- 64$ and $5$ .

$- 59 < 8 x < 40 + 5$

Step 5.3

Add $40$ and $5$ .

$- 59 < 8 x < 45$

Step 6

Divide each term in the inequality by $8$ .

$\frac{- 59}{8} < \frac{8 x}{8} < \frac{45}{8}$

Step 7

Move the negative in front of the fraction.

$- \frac{59}{8} < \frac{8 x}{8} < \frac{45}{8}$

Step 8

Cancel the common factor of $8$ .

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Step 8.1

Cancel the common factor.

$- \frac{59}{8} < \frac{8 x}{8} < \frac{45}{8}$

Step 8.2

Divide $x$ by $1$ .

$- \frac{59}{8} < x < \frac{45}{8}$

Step 9