Solve for a 2/3*(5-a)=2

$\frac{2}{3} \cdot (5 - a) = 2$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (5 - a)) = \frac{3}{2} \cdot 2$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (5 - a))$ .

Apply the distributive property.

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

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

Combine $\frac{2}{3}$ and $5$ .

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

Multiply $2$ by $5$ .

$\frac{3}{2} (\frac{10}{3} + \frac{2}{3} (- a)) = \frac{3}{2} \cdot 2$

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

$\frac{3}{2} (\frac{10}{3} - \frac{2 a}{3}) = \frac{3}{2} \cdot 2$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{10}{3} + \frac{3}{2} (- \frac{2 a}{3}) = \frac{3}{2} \cdot 2$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{10}{3} + \frac{3}{2} (- \frac{2 a}{3}) = \frac{3}{2} \cdot 2$

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2 a}{3}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 a$ .

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

Cancel the common factor.

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

Rewrite the expression.

$5 - a = \frac{3}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$5 - a = \frac{3}{2} \cdot 2$

Rewrite the expression.

$5 - a = 3$

Step 3

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

Subtract $5$ from both sides of the equation.

$- a = 3 - 5$

Subtract $5$ from $3$ .

$- a = - 2$

Step 4

Divide each term in $- a = - 2$ by $- 1$ and simplify.

Divide each term in $- a = - 2$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- 2}{- 1}$

Divide $a$ by $1$ .

$a = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$a = 2$

Solve for a 2/3*(5-a)=2

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