Solve for a 3(2/3a-1/3)=5a+3

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

Step 1

Simplify $3 (\frac{2}{3} a - \frac{1}{3})$ .

Rewrite.

$0 + 0 + 3 (\frac{2}{3} a - \frac{1}{3}) = 5 a + 3$

Simplify by adding zeros.

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

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

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$2 a - 1 = 5 a + 3$

Step 2

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

Subtract $5 a$ from both sides of the equation.

$2 a - 1 - 5 a = 3$

Subtract $5 a$ from $2 a$ .

$- 3 a - 1 = 3$

Step 3

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

Add $1$ to both sides of the equation.

$- 3 a = 3 + 1$

Add $3$ and $1$ .

$- 3 a = 4$

Step 4

Divide each term in $- 3 a = 4$ by $- 3$ and simplify.

Divide each term in $- 3 a = 4$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 1.\overline{3}$

Mixed Number Form:

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

Solve for a 3(2/3a-1/3)=5a+3

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