Pre-Algebra Examples

$7 < 1 - 7 m < 13$

Step 1

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

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Step 1.1

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$7 - 1 < - 7 m < 13 - 1$

Step 1.2

Subtract $1$ from $7$ .

$6 < - 7 m < 13 - 1$

Step 1.3

Subtract $1$ from $13$ .

$6 < - 7 m < 12$

Step 2

Divide each term in the inequality by $- 7$ .

$\frac{6}{- 7} > \frac{- 7 m}{- 7} > \frac{12}{- 7}$

Step 3

Move the negative in front of the fraction.

$- \frac{6}{7} > \frac{- 7 m}{- 7} > \frac{12}{- 7}$

Step 4

Cancel the common factor of $- 7$ .

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Step 4.1

Cancel the common factor.

$- \frac{6}{7} > \frac{- 7 m}{- 7} > \frac{12}{- 7}$

Step 4.2

Divide $m$ by $1$ .

$- \frac{6}{7} > m > \frac{12}{- 7}$

Step 5

Move the negative in front of the fraction.

$- \frac{6}{7} > m > - \frac{12}{7}$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- \frac{12}{7} < m < - \frac{6}{7}$

Step 7