Solve for m 9/8m-1/6m=-4-11/3

$\frac{9}{8} m - \frac{1}{6} m = - 4 - \frac{11}{3}$

Simplify $\frac{9}{8} m - \frac{1}{6} m$ .

Simplify each term.

Combine $\frac{9}{8}$ and $m$ .

$\frac{9 m}{8} - \frac{1}{6} m = - 4 - \frac{11}{3}$

Combine $m$ and $\frac{1}{6}$ .

$\frac{9 m}{8} - \frac{m}{6} = - 4 - \frac{11}{3}$

To write $\frac{9 m}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 m}{8} \cdot \frac{3}{3} - \frac{m}{6} = - 4 - \frac{11}{3}$

To write $- \frac{m}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9 m}{8} \cdot \frac{3}{3} - \frac{m}{6} \cdot \frac{4}{4} = - 4 - \frac{11}{3}$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9 m}{8}$ by $\frac{3}{3}$ .

$\frac{9 m \cdot 3}{8 \cdot 3} - \frac{m}{6} \cdot \frac{4}{4} = - 4 - \frac{11}{3}$

Multiply $8$ by $3$ .

$\frac{9 m \cdot 3}{24} - \frac{m}{6} \cdot \frac{4}{4} = - 4 - \frac{11}{3}$

Multiply $\frac{m}{6}$ by $\frac{4}{4}$ .

$\frac{9 m \cdot 3}{24} - \frac{m \cdot 4}{6 \cdot 4} = - 4 - \frac{11}{3}$

Multiply $6$ by $4$ .

$\frac{9 m \cdot 3}{24} - \frac{m \cdot 4}{24} = - 4 - \frac{11}{3}$

Combine the numerators over the common denominator.

$\frac{9 m \cdot 3 - m \cdot 4}{24} = - 4 - \frac{11}{3}$

Simplify the numerator.

Factor $m$ out of $9 m \cdot 3 - m \cdot 4$ .

Factor $m$ out of $9 m \cdot 3$ .

$\frac{m (9 \cdot 3) - m \cdot 4}{24} = - 4 - \frac{11}{3}$

Factor $m$ out of $- m \cdot 4$ .

$\frac{m (9 \cdot 3) + m (- 1 \cdot 4)}{24} = - 4 - \frac{11}{3}$

Factor $m$ out of $m (9 \cdot 3) + m (- 1 \cdot 4)$ .

$\frac{m (9 \cdot 3 - 1 \cdot 4)}{24} = - 4 - \frac{11}{3}$

Multiply $9$ by $3$ .

$\frac{m (27 - 1 \cdot 4)}{24} = - 4 - \frac{11}{3}$

Multiply $- 1$ by $4$ .

$\frac{m (27 - 4)}{24} = - 4 - \frac{11}{3}$

Subtract $4$ from $27$ .

$\frac{m \cdot 23}{24} = - 4 - \frac{11}{3}$

Move $23$ to the left of $m$ .

$\frac{23 m}{24} = - 4 - \frac{11}{3}$

Simplify $- 4 - \frac{11}{3}$ .

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{23 m}{24} = - 4 \cdot \frac{3}{3} - \frac{11}{3}$

Combine $- 4$ and $\frac{3}{3}$ .

$\frac{23 m}{24} = \frac{- 4 \cdot 3}{3} - \frac{11}{3}$

Combine the numerators over the common denominator.

$\frac{23 m}{24} = \frac{- 4 \cdot 3 - 11}{3}$

Simplify the numerator.

Multiply $- 4$ by $3$ .

$\frac{23 m}{24} = \frac{- 12 - 11}{3}$

Subtract $11$ from $- 12$ .

$\frac{23 m}{24} = \frac{- 23}{3}$

Move the negative in front of the fraction.

$\frac{23 m}{24} = - \frac{23}{3}$

Multiply both sides of the equation by $\frac{24}{23}$ .

$\frac{24}{23} \cdot \frac{23 m}{24} = \frac{24}{23} (- \frac{23}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{24}{23} \cdot \frac{23 m}{24}$ .

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24}{23} \cdot \frac{23 m}{24} = \frac{24}{23} (- \frac{23}{3})$

Rewrite the expression.

$\frac{1}{23} (23 m) = \frac{24}{23} (- \frac{23}{3})$

Cancel the common factor of $23$ .

Factor $23$ out of $23 m$ .

$\frac{1}{23} (23 (m)) = \frac{24}{23} (- \frac{23}{3})$

Cancel the common factor.

$\frac{1}{23} (23 m) = \frac{24}{23} (- \frac{23}{3})$

Rewrite the expression.

$m = \frac{24}{23} (- \frac{23}{3})$

Simplify the right side.

Simplify $\frac{24}{23} (- \frac{23}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{23}{3}$ into the numerator.

$m = \frac{24}{23} \cdot \frac{- 23}{3}$

Factor $3$ out of $24$ .

$m = \frac{3 (8)}{23} \cdot \frac{- 23}{3}$

Cancel the common factor.

$m = \frac{3 \cdot 8}{23} \cdot \frac{- 23}{3}$

Rewrite the expression.

$m = \frac{8}{23} \cdot - 23$

Cancel the common factor of $23$ .

Factor $23$ out of $- 23$ .

$m = \frac{8}{23} \cdot (23 (- 1))$

Cancel the common factor.

$m = \frac{8}{23} \cdot (23 \cdot - 1)$

Rewrite the expression.

$m = 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$m = - 8$

Solve for m 9/8m-1/6m=-4-11/3

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