Solve for m 1/5m+2/3-2=m-2/5

$\frac{1}{5} m + \frac{2}{3} - 2 = m - \frac{2}{5}$

Simplify $\frac{1}{5} m + \frac{2}{3} - 2$ .

Combine $\frac{1}{5}$ and $m$ .

$\frac{m}{5} + \frac{2}{3} - 2 = m - \frac{2}{5}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{m}{5} + \frac{2}{3} - 2 \cdot \frac{3}{3} = m - \frac{2}{5}$

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

$\frac{m}{5} + \frac{2}{3} + \frac{- 2 \cdot 3}{3} = m - \frac{2}{5}$

Combine the numerators over the common denominator.

$\frac{m}{5} + \frac{2 - 2 \cdot 3}{3} = m - \frac{2}{5}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$\frac{m}{5} + \frac{2 - 6}{3} = m - \frac{2}{5}$

Subtract $6$ from $2$ .

$\frac{m}{5} + \frac{- 4}{3} = m - \frac{2}{5}$

Move the negative in front of the fraction.

$\frac{m}{5} - \frac{4}{3} = m - \frac{2}{5}$

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

Subtract $m$ from both sides of the equation.

$\frac{m}{5} - \frac{4}{3} - m = - \frac{2}{5}$

To write $- m$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m}{5} - m \cdot \frac{5}{5} - \frac{4}{3} = - \frac{2}{5}$

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

$\frac{m}{5} + \frac{- m \cdot 5}{5} - \frac{4}{3} = - \frac{2}{5}$

Combine the numerators over the common denominator.

$\frac{m - m \cdot 5}{5} - \frac{4}{3} = - \frac{2}{5}$

Simplify each term.

Simplify the numerator.

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

Raise $m$ to the power of $1$ .

$\frac{m^{1} - m \cdot 5}{5} - \frac{4}{3} = - \frac{2}{5}$

Factor $m$ out of $m^{1}$ .

$\frac{m \cdot 1 - m \cdot 5}{5} - \frac{4}{3} = - \frac{2}{5}$

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

$\frac{m \cdot 1 + m (- 1 \cdot 5)}{5} - \frac{4}{3} = - \frac{2}{5}$

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

$\frac{m (1 - 1 \cdot 5)}{5} - \frac{4}{3} = - \frac{2}{5}$

Multiply $- 1$ by $5$ .

$\frac{m (1 - 5)}{5} - \frac{4}{3} = - \frac{2}{5}$

Subtract $5$ from $1$ .

$\frac{m \cdot - 4}{5} - \frac{4}{3} = - \frac{2}{5}$

Move $- 4$ to the left of $m$ .

$\frac{- 4 \cdot m}{5} - \frac{4}{3} = - \frac{2}{5}$

Move the negative in front of the fraction.

$- \frac{4 m}{5} - \frac{4}{3} = - \frac{2}{5}$

Move all terms not containing $m$ to the right side of the equation.

Add $\frac{4}{3}$ to both sides of the equation.

$- \frac{4 m}{5} = - \frac{2}{5} + \frac{4}{3}$

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 m}{5} = - \frac{2}{5} \cdot \frac{3}{3} + \frac{4}{3}$

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4 m}{5} = - \frac{2}{5} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{5}{5}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$- \frac{4 m}{5} = - \frac{2 \cdot 3}{5 \cdot 3} + \frac{4}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$- \frac{4 m}{5} = - \frac{2 \cdot 3}{15} + \frac{4}{3} \cdot \frac{5}{5}$

Multiply $\frac{4}{3}$ by $\frac{5}{5}$ .

$- \frac{4 m}{5} = - \frac{2 \cdot 3}{15} + \frac{4 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$- \frac{4 m}{5} = - \frac{2 \cdot 3}{15} + \frac{4 \cdot 5}{15}$

Combine the numerators over the common denominator.

$- \frac{4 m}{5} = \frac{- 2 \cdot 3 + 4 \cdot 5}{15}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$- \frac{4 m}{5} = \frac{- 6 + 4 \cdot 5}{15}$

Multiply $4$ by $5$ .

$- \frac{4 m}{5} = \frac{- 6 + 20}{15}$

Add $- 6$ and $20$ .

$- \frac{4 m}{5} = \frac{14}{15}$

Multiply both sides of the equation by $- \frac{5}{4}$ .

$- \frac{5}{4} (- \frac{4 m}{5}) = - \frac{5}{4} \cdot \frac{14}{15}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{4} (- \frac{4 m}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{- 5}{4} (- \frac{4 m}{5}) = - \frac{5}{4} \cdot \frac{14}{15}$

Move the leading negative in $- \frac{4 m}{5}$ into the numerator.

$\frac{- 5}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{14}{15}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{14}{15}$

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{14}{15}$

Rewrite the expression.

$\frac{- 1}{4} (- 4 m) = - \frac{5}{4} \cdot \frac{14}{15}$

Cancel the common factor of $4$ .

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

$\frac{- 1}{4} (4 (- m)) = - \frac{5}{4} \cdot \frac{14}{15}$

Cancel the common factor.

$\frac{- 1}{4} (4 (- m)) = - \frac{5}{4} \cdot \frac{14}{15}$

Rewrite the expression.

$- - m = - \frac{5}{4} \cdot \frac{14}{15}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{5}{4} \cdot \frac{14}{15}$

Multiply $m$ by $1$ .

$m = - \frac{5}{4} \cdot \frac{14}{15}$

Simplify the right side.

Simplify $- \frac{5}{4} \cdot \frac{14}{15}$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$m = \frac{- 5}{4} \cdot \frac{14}{15}$

Factor $5$ out of $- 5$ .

$m = \frac{5 (- 1)}{4} \cdot \frac{14}{15}$

Factor $5$ out of $15$ .

$m = \frac{5 \cdot - 1}{4} \cdot \frac{14}{5 \cdot 3}$

Cancel the common factor.

$m = \frac{5 \cdot - 1}{4} \cdot \frac{14}{5 \cdot 3}$

Rewrite the expression.

$m = \frac{- 1}{4} \cdot \frac{14}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$m = \frac{- 1}{2 (2)} \cdot \frac{14}{3}$

Factor $2$ out of $14$ .

$m = \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 7}{3}$

Cancel the common factor.

$m = \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 7}{3}$

Rewrite the expression.

$m = \frac{- 1}{2} \cdot \frac{7}{3}$

Multiply $\frac{- 1}{2}$ by $\frac{7}{3}$ .

$m = \frac{- 1 \cdot 7}{2 \cdot 3}$

Simplify the expression.

Multiply $- 1$ by $7$ .

$m = \frac{- 7}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{- 7}{6}$

Move the negative in front of the fraction.

$m = - \frac{7}{6}$

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{7}{6}$

Decimal Form:

$m = - 1.1\overline{6}$

Mixed Number Form:

$m = - 1 \frac{1}{6}$

Solve for m 1/5m+2/3-2=m-2/5

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