Solve for x 2/3x-5/6=-1/2

$\frac{2}{3} x - \frac{5}{6} = - \frac{1}{2}$

Step 1

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

$\frac{2 x}{3} - \frac{5}{6} = - \frac{1}{2}$

Step 2

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

Add $\frac{5}{6}$ to both sides of the equation.

$\frac{2 x}{3} = - \frac{1}{2} + \frac{5}{6}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} = - \frac{1}{2} \cdot \frac{3}{3} + \frac{5}{6}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{2 x}{3} = - \frac{3}{2 \cdot 3} + \frac{5}{6}$

Multiply $2$ by $3$ .

$\frac{2 x}{3} = - \frac{3}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{2 x}{3} = \frac{- 3 + 5}{6}$

Add $- 3$ and $5$ .

$\frac{2 x}{3} = \frac{2}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 x}{3} = \frac{2 \cdot 1}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 x}{3} = \frac{2 \cdot 1}{2 \cdot 3}$

Rewrite the expression.

$\frac{2 x}{3} = \frac{1}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 x = 1$

Step 4

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

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x 2/3x-5/6=-1/2

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