Solve for m 4/3m=-m+5/3m+3

$\frac{4}{3} m = - m + \frac{5}{3} m + 3$

Since $m$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- m + \frac{5}{3} m + 3 = \frac{4}{3} m$

Simplify $- m + \frac{5}{3} m + 3$ .

Combine $\frac{5}{3}$ and $m$ .

$- m + \frac{5 m}{3} + 3 = \frac{4}{3} m$

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

$- m \cdot \frac{3}{3} + \frac{5 m}{3} + 3 = \frac{4}{3} m$

Simplify terms.

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

$\frac{- m \cdot 3}{3} + \frac{5 m}{3} + 3 = \frac{4}{3} m$

Combine the numerators over the common denominator.

$\frac{- m \cdot 3 + 5 m}{3} + 3 = \frac{4}{3} m$

Simplify each term.

Simplify the numerator.

Factor $m$ out of $- m \cdot 3 + 5 m$ .

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

$\frac{m (- 1 \cdot 3) + 5 m}{3} + 3 = \frac{4}{3} m$

Factor $m$ out of $5 m$ .

$\frac{m (- 1 \cdot 3) + m \cdot 5}{3} + 3 = \frac{4}{3} m$

Factor $m$ out of $m (- 1 \cdot 3) + m \cdot 5$ .

$\frac{m (- 1 \cdot 3 + 5)}{3} + 3 = \frac{4}{3} m$

Multiply $- 1$ by $3$ .

$\frac{m (- 3 + 5)}{3} + 3 = \frac{4}{3} m$

Add $- 3$ and $5$ .

$\frac{m \cdot 2}{3} + 3 = \frac{4}{3} m$

Move $2$ to the left of $m$ .

$\frac{2 m}{3} + 3 = \frac{4}{3} m$

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

$\frac{2 m}{3} + 3 = \frac{4 m}{3}$

Move all terms containing $m$ to the left side of the equation.

Subtract $\frac{4 m}{3}$ from both sides of the equation.

$\frac{2 m}{3} + 3 - \frac{4 m}{3} = 0$

Combine the numerators over the common denominator.

$3 + \frac{2 m - 4 m}{3} = 0$

Subtract $4 m$ from $2 m$ .

$3 + \frac{- 2 m}{3} = 0$

Move the negative in front of the fraction.

$3 - \frac{2 m}{3} = 0$

Subtract $3$ from both sides of the equation.

$- \frac{2 m}{3} = - 3$

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 m}{3}) = - \frac{3}{2} \cdot - 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 m}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 m}{3}) = - \frac{3}{2} \cdot - 3$

Move the leading negative in $- \frac{2 m}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 m}{3} = - \frac{3}{2} \cdot - 3$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 m}{3} = - \frac{3}{2} \cdot - 3$

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 m}{3} = - \frac{3}{2} \cdot - 3$

Rewrite the expression.

$\frac{- 1}{2} (- 2 m) = - \frac{3}{2} \cdot - 3$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 m$ .

$\frac{- 1}{2} (2 (- m)) = - \frac{3}{2} \cdot - 3$

Cancel the common factor.

$\frac{- 1}{2} (2 (- m)) = - \frac{3}{2} \cdot - 3$

Rewrite the expression.

$- - m = - \frac{3}{2} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{3}{2} \cdot - 3$

Multiply $m$ by $1$ .

$m = - \frac{3}{2} \cdot - 3$

Simplify the right side.

Multiply $- \frac{3}{2} \cdot - 3$ .

Multiply $- 3$ by $- 1$ .

$m = 3 (\frac{3}{2})$

Combine $3$ and $\frac{3}{2}$ .

$m = \frac{3 \cdot 3}{2}$

Multiply $3$ by $3$ .

$m = \frac{9}{2}$

The result can be shown in multiple forms.

Exact Form:

$m = \frac{9}{2}$

Decimal Form:

$m = 4.5$

Mixed Number Form:

$m = 4 \frac{1}{2}$

Solve for m 4/3m=-m+5/3m+3

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