Solve for x 5/8(x-1/3)=5/12

$\frac{5}{8} (x - \frac{1}{3}) = \frac{5}{12}$

Step 1

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} (\frac{5}{8} \cdot (x - \frac{1}{3})) = \frac{8}{5} \cdot \frac{5}{12}$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{5} (\frac{5}{8} \cdot (x - \frac{1}{3}))$ .

Apply the distributive property.

$\frac{8}{5} (\frac{5}{8} x + \frac{5}{8} (- \frac{1}{3})) = \frac{8}{5} \cdot \frac{5}{12}$

Combine $\frac{5}{8}$ and $x$ .

$\frac{8}{5} (\frac{5 x}{8} + \frac{5}{8} (- \frac{1}{3})) = \frac{8}{5} \cdot \frac{5}{12}$

Multiply $\frac{5}{8} (- \frac{1}{3})$ .

Multiply $\frac{5}{8}$ by $\frac{1}{3}$ .

$\frac{8}{5} (\frac{5 x}{8} - \frac{5}{8 \cdot 3}) = \frac{8}{5} \cdot \frac{5}{12}$

Multiply $8$ by $3$ .

$\frac{8}{5} (\frac{5 x}{8} - \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Apply the distributive property.

$\frac{8}{5} \cdot \frac{5 x}{8} + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 x}{8} + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Rewrite the expression.

$\frac{1}{5} (5 x) + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Rewrite the expression.

$x + \frac{8}{5} (- \frac{5}{24}) = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{5}{24}$ into the numerator.

$x + \frac{8}{5} \cdot \frac{- 5}{24} = \frac{8}{5} \cdot \frac{5}{12}$

Factor $8$ out of $24$ .

$x + \frac{8}{5} \cdot \frac{- 5}{8 (3)} = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor.

$x + \frac{8}{5} \cdot \frac{- 5}{8 \cdot 3} = \frac{8}{5} \cdot \frac{5}{12}$

Rewrite the expression.

$x + \frac{1}{5} \cdot \frac{- 5}{3} = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$x + \frac{1}{5} \cdot \frac{5 (- 1)}{3} = \frac{8}{5} \cdot \frac{5}{12}$

Cancel the common factor.

$x + \frac{1}{5} \cdot \frac{5 \cdot - 1}{3} = \frac{8}{5} \cdot \frac{5}{12}$

Rewrite the expression.

$x + \frac{- 1}{3} = \frac{8}{5} \cdot \frac{5}{12}$

Move the negative in front of the fraction.

$x - \frac{1}{3} = \frac{8}{5} \cdot \frac{5}{12}$

Simplify the right side.

Simplify $\frac{8}{5} \cdot \frac{5}{12}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x - \frac{1}{3} = \frac{4 (2)}{5} \cdot \frac{5}{12}$

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine $2$ and $\frac{1}{3}$ .

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

Step 3

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

Add $\frac{1}{3}$ to both sides of the equation.

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

Divide $3$ by $3$ .

$x = 1$

Solve for x 5/8(x-1/3)=5/12

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