Solve for x 2/3(x-5/4)=-1/3

$\frac{2}{3} (x - \frac{5}{4}) = - \frac{1}{3}$

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

$\frac{3}{2} (\frac{2}{3} \cdot (x - \frac{5}{4})) = \frac{3}{2} (- \frac{1}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (x - \frac{5}{4}))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} x + \frac{2}{3} (- \frac{5}{4})) = \frac{3}{2} (- \frac{1}{3})$

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

$\frac{3}{2} (\frac{2 x}{3} + \frac{2}{3} (- \frac{5}{4})) = \frac{3}{2} (- \frac{1}{3})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{3}{2} (\frac{2 x}{3} + \frac{2}{3} \cdot \frac{- 5}{4}) = \frac{3}{2} (- \frac{1}{3})$

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{3}$ by $\frac{- 5}{2}$ .

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

Simplify the expression.

Multiply $3$ by $2$ .

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

Move the negative in front of the fraction.

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

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

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{2}$ by $\frac{- 5}{2}$ .

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

Simplify the expression.

Multiply $2$ by $2$ .

$x + \frac{- 5}{4} = \frac{3}{2} (- \frac{1}{3})$

Move the negative in front of the fraction.

$x - \frac{5}{4} = \frac{3}{2} (- \frac{1}{3})$

Simplify the right side.

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

Cancel the common factor of $3$ .

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

$x - \frac{5}{4} = \frac{3}{2} \cdot \frac{- 1}{3}$

Cancel the common factor.

$x - \frac{5}{4} = \frac{3}{2} \cdot \frac{- 1}{3}$

Rewrite the expression.

$x - \frac{5}{4} = \frac{1}{2} \cdot - 1$

Combine $\frac{1}{2}$ and $- 1$ .

$x - \frac{5}{4} = \frac{- 1}{2}$

Move the negative in front of the fraction.

$x - \frac{5}{4} = - \frac{1}{2}$

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

Add $\frac{5}{4}$ to both sides of the equation.

$x = - \frac{1}{2} + \frac{5}{4}$

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

$x = - \frac{1}{2} \cdot \frac{2}{2} + \frac{5}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$x = - \frac{2}{2 \cdot 2} + \frac{5}{4}$

Multiply $2$ by $2$ .

$x = - \frac{2}{4} + \frac{5}{4}$

Combine the numerators over the common denominator.

$x = \frac{- 2 + 5}{4}$

Add $- 2$ and $5$ .

$x = \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$

Solve for x 2/3(x-5/4)=-1/3

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