Algebra Examples

$4 - \frac{3}{5} m = \frac{6}{5} m + 2$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$4 - \frac{m \cdot 3}{5} = \frac{6}{5} m + 2$

Step 1.2

Move $3$ to the left of $m$ .

$4 - \frac{3 m}{5} = \frac{6}{5} m + 2$

Step 2

Combine $\frac{6}{5}$ and $m$ .

$4 - \frac{3 m}{5} = \frac{6 m}{5} + 2$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{6 m}{5}$ from both sides of the equation.

$4 - \frac{3 m}{5} - \frac{6 m}{5} = 2$

Step 3.2

Combine the numerators over the common denominator.

$4 + \frac{- 3 m - 6 m}{5} = 2$

Step 3.3

Subtract $6 m$ from $- 3 m$ .

$4 + \frac{- 9 m}{5} = 2$

Step 3.4

Move the negative in front of the fraction.

$4 - \frac{9 m}{5} = 2$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $4$ from both sides of the equation.

$- \frac{9 m}{5} = 2 - 4$

Step 4.2

Subtract $4$ from $2$ .

$- \frac{9 m}{5} = - 2$

Step 5

Multiply both sides of the equation by $- \frac{5}{9}$ .

$- \frac{5}{9} (- \frac{9 m}{5}) = - \frac{5}{9} \cdot - 2$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- \frac{5}{9} (- \frac{9 m}{5})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$\frac{- 5}{9} (- \frac{9 m}{5}) = - \frac{5}{9} \cdot - 2$

Step 6.1.1.1.2

Move the leading negative in $- \frac{9 m}{5}$ into the numerator.

$\frac{- 5}{9} \cdot \frac{- 9 m}{5} = - \frac{5}{9} \cdot - 2$

Step 6.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{9} \cdot \frac{- 9 m}{5} = - \frac{5}{9} \cdot - 2$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{9} \cdot \frac{- 9 m}{5} = - \frac{5}{9} \cdot - 2$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{9} (- 9 m) = - \frac{5}{9} \cdot - 2$

Step 6.1.1.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $9$ out of $- 9 m$ .

$\frac{- 1}{9} (9 (- m)) = - \frac{5}{9} \cdot - 2$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{9} (9 (- m)) = - \frac{5}{9} \cdot - 2$

Step 6.1.1.2.3

Rewrite the expression.

$- - m = - \frac{5}{9} \cdot - 2$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{5}{9} \cdot - 2$

Step 6.1.1.3.2

Multiply $m$ by $1$ .

$m = - \frac{5}{9} \cdot - 2$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Multiply $- \frac{5}{9} \cdot - 2$ .

Tap for more steps...

Step 6.2.1.1

Multiply $- 2$ by $- 1$ .

$m = 2 (\frac{5}{9})$

Step 6.2.1.2

Combine $2$ and $\frac{5}{9}$ .

$m = \frac{2 \cdot 5}{9}$

Step 6.2.1.3

Multiply $2$ by $5$ .

$m = \frac{10}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = \frac{10}{9}$

Decimal Form:

$m = 1.\overline{1}$

Mixed Number Form:

$m = 1 \frac{1}{9}$