Solve for a -1/5-4/9a=2/15

$- \frac{1}{5} - \frac{4}{9} a = \frac{2}{15}$

Simplify each term.

Combine $a$ and $\frac{4}{9}$ .

$- \frac{1}{5} - \frac{a \cdot 4}{9} = \frac{2}{15}$

Move $4$ to the left of $a$ .

$- \frac{1}{5} - \frac{4 a}{9} = \frac{2}{15}$

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

Add $\frac{1}{5}$ to both sides of the equation.

$- \frac{4 a}{9} = \frac{2}{15} + \frac{1}{5}$

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 a}{9} = \frac{2}{15} + \frac{1}{5} \cdot \frac{3}{3}$

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

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$- \frac{4 a}{9} = \frac{2}{15} + \frac{3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$- \frac{4 a}{9} = \frac{2}{15} + \frac{3}{15}$

Combine the numerators over the common denominator.

$- \frac{4 a}{9} = \frac{2 + 3}{15}$

Add $2$ and $3$ .

$- \frac{4 a}{9} = \frac{5}{15}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5$ .

$- \frac{4 a}{9} = \frac{5 (1)}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

$- \frac{4 a}{9} = \frac{5 \cdot 1}{5 \cdot 3}$

Cancel the common factor.

$- \frac{4 a}{9} = \frac{5 \cdot 1}{5 \cdot 3}$

Rewrite the expression.

$- \frac{4 a}{9} = \frac{1}{3}$

Multiply both sides of the equation by $- \frac{9}{4}$ .

$- \frac{9}{4} (- \frac{4 a}{9}) = - \frac{9}{4} \cdot \frac{1}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{9}{4} (- \frac{4 a}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$\frac{- 9}{4} (- \frac{4 a}{9}) = - \frac{9}{4} \cdot \frac{1}{3}$

Move the leading negative in $- \frac{4 a}{9}$ into the numerator.

$\frac{- 9}{4} \cdot \frac{- 4 a}{9} = - \frac{9}{4} \cdot \frac{1}{3}$

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{4} \cdot \frac{- 4 a}{9} = - \frac{9}{4} \cdot \frac{1}{3}$

Cancel the common factor.

$\frac{9 \cdot - 1}{4} \cdot \frac{- 4 a}{9} = - \frac{9}{4} \cdot \frac{1}{3}$

Rewrite the expression.

$\frac{- 1}{4} (- 4 a) = - \frac{9}{4} \cdot \frac{1}{3}$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 a$ .

$\frac{- 1}{4} (4 (- a)) = - \frac{9}{4} \cdot \frac{1}{3}$

Cancel the common factor.

$\frac{- 1}{4} (4 (- a)) = - \frac{9}{4} \cdot \frac{1}{3}$

Rewrite the expression.

$- - a = - \frac{9}{4} \cdot \frac{1}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 a = - \frac{9}{4} \cdot \frac{1}{3}$

Multiply $a$ by $1$ .

$a = - \frac{9}{4} \cdot \frac{1}{3}$

Simplify the right side.

Simplify $- \frac{9}{4} \cdot \frac{1}{3}$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$a = \frac{- 9}{4} \cdot \frac{1}{3}$

Factor $3$ out of $- 9$ .

$a = \frac{3 (- 3)}{4} \cdot \frac{1}{3}$

Cancel the common factor.

$a = \frac{3 \cdot - 3}{4} \cdot \frac{1}{3}$

Rewrite the expression.

$a = \frac{- 3}{4}$

Move the negative in front of the fraction.

$a = - \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{3}{4}$

Decimal Form:

$a = - 0.75$

Solve for a -1/5-4/9a=2/15

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