Pre-Algebra Examples

$- 5 < 8 x + 6 > 7$

Step 1

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

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Step 1.1

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 6 < 8 x > 7 - 6$

Step 1.2

Subtract $6$ from $- 5$ .

$- 11 < 8 x > 7 - 6$

Step 1.3

Subtract $6$ from $7$ .

$- 11 < 8 x > 1$

Step 2

Divide each term in the inequality by $8$ .

$\frac{- 11}{8} < \frac{8 x}{8} > \frac{1}{8}$

Step 3

Move the negative in front of the fraction.

$- \frac{11}{8} < \frac{8 x}{8} > \frac{1}{8}$

Step 4

Cancel the common factor of $8$ .

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Step 4.1

Cancel the common factor.

$- \frac{11}{8} < \frac{8 x}{8} > \frac{1}{8}$

Step 4.2

Divide $x$ by $1$ .

$- \frac{11}{8} < x > \frac{1}{8}$

Step 5

Since $x > - \frac{11}{8}$ covers the entire solution set, drop the rest of the interval from the solution.

$x > - \frac{11}{8}$

Step 6