Solve for m 1/10m+1/2=-1/2m-1/2

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

Step 1

Combine $\frac{1}{10}$ and $m$ .

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

Step 2

Combine $m$ and $\frac{1}{2}$ .

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

Step 3

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

Add $\frac{m}{2}$ to both sides of the equation.

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

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

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

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

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

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

Multiply $2$ by $5$ .

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

Combine the numerators over the common denominator.

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

Add $m$ and $m \cdot 5$ .

Reorder $m$ and $5$ .

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

Add $m$ and $5 \cdot m$ .

$\frac{6 m}{10} + \frac{1}{2} = - \frac{1}{2}$

Cancel the common factor of $6$ and $10$ .

Factor $2$ out of $6 m$ .

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

Cancel the common factors.

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $- 1$ .

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

Divide $- 2$ by $2$ .

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

Step 5

Multiply both sides of the equation by $\frac{5}{3}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{3} \cdot \frac{3 m}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 m$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{5}{3} \cdot - 1$ .

Multiply $\frac{5}{3} \cdot - 1$ .

Combine $\frac{5}{3}$ and $- 1$ .

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

Multiply $5$ by $- 1$ .

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

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$m = - 1.\overline{6}$

Mixed Number Form:

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

Solve for m 1/10m+1/2=-1/2m-1/2

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