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

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

Step 1

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

Simplify each term.

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

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

Combine $m$ and $\frac{5}{2}$ .

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

Move $5$ to the left of $m$ .

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

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

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

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

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $2$ .

$\frac{3 m \cdot 2}{10} - \frac{5 m}{2} \cdot \frac{5}{5} - 2 = - m - 1 + \frac{1}{5} m$

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

$\frac{3 m \cdot 2}{10} - \frac{5 m \cdot 5}{2 \cdot 5} - 2 = - m - 1 + \frac{1}{5} m$

Multiply $2$ by $5$ .

$\frac{3 m \cdot 2}{10} - \frac{5 m \cdot 5}{10} - 2 = - m - 1 + \frac{1}{5} m$

Combine the numerators over the common denominator.

$\frac{3 m \cdot 2 - 5 m \cdot 5}{10} - 2 = - m - 1 + \frac{1}{5} m$

Simplify each term.

Simplify the numerator.

Factor $m$ out of $3 m \cdot 2 - 5 m \cdot 5$ .

Factor $m$ out of $3 m \cdot 2$ .

$\frac{m (3 \cdot 2) - 5 m \cdot 5}{10} - 2 = - m - 1 + \frac{1}{5} m$

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

$\frac{m (3 \cdot 2) + m (- 5 \cdot 5)}{10} - 2 = - m - 1 + \frac{1}{5} m$

Factor $m$ out of $m (3 \cdot 2) + m (- 5 \cdot 5)$ .

$\frac{m (3 \cdot 2 - 5 \cdot 5)}{10} - 2 = - m - 1 + \frac{1}{5} m$

Multiply $3$ by $2$ .

$\frac{m (6 - 5 \cdot 5)}{10} - 2 = - m - 1 + \frac{1}{5} m$

Multiply $- 5$ by $5$ .

$\frac{m (6 - 25)}{10} - 2 = - m - 1 + \frac{1}{5} m$

Subtract $25$ from $6$ .

$\frac{m \cdot - 19}{10} - 2 = - m - 1 + \frac{1}{5} m$

Move $- 19$ to the left of $m$ .

$\frac{- 19 \cdot m}{10} - 2 = - m - 1 + \frac{1}{5} m$

Move the negative in front of the fraction.

$- \frac{19 m}{10} - 2 = - m - 1 + \frac{1}{5} m$

Step 2

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

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

$- \frac{19 m}{10} - 2 = - m - 1 + \frac{m}{5}$

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

$- \frac{19 m}{10} - 2 = - m \cdot \frac{5}{5} + \frac{m}{5} - 1$

Simplify terms.

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

$- \frac{19 m}{10} - 2 = \frac{- m \cdot 5}{5} + \frac{m}{5} - 1$

Combine the numerators over the common denominator.

$- \frac{19 m}{10} - 2 = \frac{- m \cdot 5 + m}{5} - 1$

Simplify each term.

Simplify the numerator.

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

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

$- \frac{19 m}{10} - 2 = \frac{m (- 1 \cdot 5) + m}{5} - 1$

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

$- \frac{19 m}{10} - 2 = \frac{m (- 1 \cdot 5) + m^{1}}{5} - 1$

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

$- \frac{19 m}{10} - 2 = \frac{m (- 1 \cdot 5) + m \cdot 1}{5} - 1$

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

$- \frac{19 m}{10} - 2 = \frac{m (- 1 \cdot 5 + 1)}{5} - 1$

Multiply $- 1$ by $5$ .

$- \frac{19 m}{10} - 2 = \frac{m (- 5 + 1)}{5} - 1$

Add $- 5$ and $1$ .

$- \frac{19 m}{10} - 2 = \frac{m \cdot - 4}{5} - 1$

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

$- \frac{19 m}{10} - 2 = \frac{- 4 \cdot m}{5} - 1$

Move the negative in front of the fraction.

$- \frac{19 m}{10} - 2 = - \frac{4 m}{5} - 1$

Step 3

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

Add $\frac{4 m}{5}$ to both sides of the equation.

$- \frac{19 m}{10} - 2 + \frac{4 m}{5} = - 1$

To write $\frac{4 m}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{19 m}{10} + \frac{4 m}{5} \cdot \frac{2}{2} - 2 = - 1$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 m}{5}$ by $\frac{2}{2}$ .

$- \frac{19 m}{10} + \frac{4 m \cdot 2}{5 \cdot 2} - 2 = - 1$

Multiply $5$ by $2$ .

$- \frac{19 m}{10} + \frac{4 m \cdot 2}{10} - 2 = - 1$

Combine the numerators over the common denominator.

$\frac{- 19 m + 4 m \cdot 2}{10} - 2 = - 1$

Simplify each term.

Simplify the numerator.

Factor $m$ out of $- 19 m + 4 m \cdot 2$ .

Factor $m$ out of $- 19 m$ .

$\frac{m \cdot - 19 + 4 m \cdot 2}{10} - 2 = - 1$

Factor $m$ out of $4 m \cdot 2$ .

$\frac{m \cdot - 19 + m (4 \cdot 2)}{10} - 2 = - 1$

Factor $m$ out of $m \cdot - 19 + m (4 \cdot 2)$ .

$\frac{m (- 19 + 4 \cdot 2)}{10} - 2 = - 1$

Multiply $4$ by $2$ .

$\frac{m (- 19 + 8)}{10} - 2 = - 1$

Add $- 19$ and $8$ .

$\frac{m \cdot - 11}{10} - 2 = - 1$

Move $- 11$ to the left of $m$ .

$\frac{- 11 \cdot m}{10} - 2 = - 1$

Move the negative in front of the fraction.

$- \frac{11 m}{10} - 2 = - 1$

Step 4

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

Add $2$ to both sides of the equation.

$- \frac{11 m}{10} = - 1 + 2$

Add $- 1$ and $2$ .

$- \frac{11 m}{10} = 1$

Step 5

Multiply both sides of the equation by $- \frac{10}{11}$ .

$- \frac{10}{11} (- \frac{11 m}{10}) = - \frac{10}{11} \cdot 1$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{10}{11} (- \frac{11 m}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{10}{11}$ into the numerator.

$\frac{- 10}{11} (- \frac{11 m}{10}) = - \frac{10}{11} \cdot 1$

Move the leading negative in $- \frac{11 m}{10}$ into the numerator.

$\frac{- 10}{11} \cdot \frac{- 11 m}{10} = - \frac{10}{11} \cdot 1$

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{11} \cdot \frac{- 11 m}{10} = - \frac{10}{11} \cdot 1$

Cancel the common factor.

$\frac{10 \cdot - 1}{11} \cdot \frac{- 11 m}{10} = - \frac{10}{11} \cdot 1$

Rewrite the expression.

$\frac{- 1}{11} (- 11 m) = - \frac{10}{11} \cdot 1$

Cancel the common factor of $11$ .

Factor $11$ out of $- 11 m$ .

$\frac{- 1}{11} (11 (- m)) = - \frac{10}{11} \cdot 1$

Cancel the common factor.

$\frac{- 1}{11} (11 (- m)) = - \frac{10}{11} \cdot 1$

Rewrite the expression.

$- - m = - \frac{10}{11} \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{10}{11} \cdot 1$

Multiply $m$ by $1$ .

$m = - \frac{10}{11} \cdot 1$

Simplify the right side.

Multiply $- 1$ by $1$ .

$m = - \frac{10}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{10}{11}$

Decimal Form:

$m = - 0.\overline{90}$

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

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