Solve for a a/6-2/3=(5a)/18

$\frac{a}{6} - \frac{2}{3} = \frac{5 a}{18}$

Step 1

Multiply both sides by $18$ .

$(\frac{a}{6} - \frac{2}{3}) \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{a}{6} - \frac{2}{3}) \cdot 18$ .

Simplify terms.

Apply the distributive property.

$\frac{a}{6} \cdot 18 - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Cancel the common factor of $6$ .

Factor $6$ out of $18$ .

$\frac{a}{6} \cdot (6 (3)) - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Cancel the common factor.

$\frac{a}{6} \cdot (6 \cdot 3) - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Rewrite the expression.

$a \cdot 3 - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Cancel the common factor of $3$ .

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

$a \cdot 3 + \frac{- 2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Factor $3$ out of $18$ .

$a \cdot 3 + \frac{- 2}{3} \cdot (3 (6)) = \frac{5 a}{18} \cdot 18$

Cancel the common factor.

$a \cdot 3 + \frac{- 2}{3} \cdot (3 \cdot 6) = \frac{5 a}{18} \cdot 18$

Rewrite the expression.

$a \cdot 3 - 2 \cdot 6 = \frac{5 a}{18} \cdot 18$

Multiply $- 2$ by $6$ .

$a \cdot 3 - 12 = \frac{5 a}{18} \cdot 18$

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

$3 a - 12 = \frac{5 a}{18} \cdot 18$

Simplify the right side.

Cancel the common factor of $18$ .

Cancel the common factor.

$3 a - 12 = \frac{5 a}{18} \cdot 18$

Rewrite the expression.

$3 a - 12 = 5 a$

Step 3

Solve for $a$ .

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

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

$3 a - 12 - 5 a = 0$

Subtract $5 a$ from $3 a$ .

$- 2 a - 12 = 0$

Add $12$ to both sides of the equation.

$- 2 a = 12$

Divide each term in $- 2 a = 12$ by $- 2$ and simplify.

Divide each term in $- 2 a = 12$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{12}{- 2}$

Divide $a$ by $1$ .

$a = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$a = - 6$

Solve for a a/6-2/3=(5a)/18

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