Solve for m 9<15mx-8<27

$9 < 15 m x - 8 < 27$

Step 1

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

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

$9 + 8 < 15 m x < 27 + 8$

Add $9$ and $8$ .

$17 < 15 m x < 27 + 8$

Add $27$ and $8$ .

$17 < 15 m x < 35$

Step 2

Divide each term in the inequality by $15 x$ .

$\frac{17}{15 x} < \frac{15 m x}{15 x} < \frac{35}{15 x}$

Step 3

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{17}{15 x} < \frac{15 m x}{15 x} < \frac{35}{15 x}$

Rewrite the expression.

$\frac{17}{15 x} < \frac{m x}{x} < \frac{35}{15 x}$

Step 4

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{17}{15 x} < \frac{m x}{x} < \frac{35}{15 x}$

Divide $m$ by $1$ .

$\frac{17}{15 x} < m < \frac{35}{15 x}$

Step 5

Cancel the common factor of $35$ and $15$ .

Factor $5$ out of $35$ .

$\frac{17}{15 x} < m < \frac{5 (7)}{15 x}$

Cancel the common factors.

Factor $5$ out of $15 x$ .

$\frac{17}{15 x} < m < \frac{5 (7)}{5 (3 x)}$

Cancel the common factor.

$\frac{17}{15 x} < m < \frac{5 \cdot 7}{5 (3 x)}$

Rewrite the expression.

$\frac{17}{15 x} < m < \frac{7}{3 x}$

Step 6