Find All Complex Solutions (3x)/2+1/6=(2x)/3-2/3

$\frac{3 x}{2} + \frac{1}{6} = \frac{2 x}{3} - \frac{2}{3}$

Step 1

Multiply each term in $\frac{3 x}{2} + \frac{1}{6} = \frac{2 x}{3} - \frac{2}{3}$ by $6$ to eliminate the fractions.

Multiply each term in $\frac{3 x}{2} + \frac{1}{6} = \frac{2 x}{3} - \frac{2}{3}$ by $6$ .

$\frac{3 x}{2} \cdot 6 + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{3 x}{2} \cdot (2 (3)) + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Cancel the common factor.

$\frac{3 x}{2} \cdot (2 \cdot 3) + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Rewrite the expression.

$3 x \cdot 3 + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Multiply $3$ by $3$ .

$9 x + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Cancel the common factor of $6$ .

Cancel the common factor.

$9 x + \frac{1}{6} \cdot 6 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Rewrite the expression.

$9 x + 1 = \frac{2 x}{3} \cdot 6 - \frac{2}{3} \cdot 6$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$9 x + 1 = \frac{2 x}{3} \cdot (3 (2)) - \frac{2}{3} \cdot 6$

Cancel the common factor.

$9 x + 1 = \frac{2 x}{3} \cdot (3 \cdot 2) - \frac{2}{3} \cdot 6$

Rewrite the expression.

$9 x + 1 = 2 x \cdot 2 - \frac{2}{3} \cdot 6$

Multiply $2$ by $2$ .

$9 x + 1 = 4 x - \frac{2}{3} \cdot 6$

Cancel the common factor of $3$ .

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

$9 x + 1 = 4 x + \frac{- 2}{3} \cdot 6$

Factor $3$ out of $6$ .

$9 x + 1 = 4 x + \frac{- 2}{3} \cdot (3 (2))$

Cancel the common factor.

$9 x + 1 = 4 x + \frac{- 2}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$9 x + 1 = 4 x - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$9 x + 1 = 4 x - 4$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$9 x + 1 - 4 x = - 4$

Subtract $4 x$ from $9 x$ .

$5 x + 1 = - 4$

Step 3

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

Subtract $1$ from both sides of the equation.

$5 x = - 4 - 1$

Subtract $1$ from $- 4$ .

$5 x = - 5$

Step 4

Divide each term in $5 x = - 5$ by $5$ and simplify.

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

Find All Complex Solutions (3x)/2+1/6=(2x)/3-2/3

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