Solve for x 5/6(3/8-x)=16

$\frac{5}{6} (\frac{3}{8} - x) = 16$

Step 1

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} (\frac{5}{6} \cdot (\frac{3}{8} - x)) = \frac{6}{5} \cdot 16$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} (\frac{5}{6} \cdot (\frac{3}{8} - x))$ .

Apply the distributive property.

$\frac{6}{5} (\frac{5}{6} \cdot \frac{3}{8} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{6}{5} (\frac{5}{3 (2)} \cdot \frac{3}{8} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Cancel the common factor.

$\frac{6}{5} (\frac{5}{3 \cdot 2} \cdot \frac{3}{8} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Rewrite the expression.

$\frac{6}{5} (\frac{5}{2} \cdot \frac{1}{8} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Multiply $\frac{5}{2}$ by $\frac{1}{8}$ .

$\frac{6}{5} (\frac{5}{2 \cdot 8} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Multiply $2$ by $8$ .

$\frac{6}{5} (\frac{5}{16} + \frac{5}{6} (- x)) = \frac{6}{5} \cdot 16$

Combine $\frac{5}{6}$ and $x$ .

$\frac{6}{5} (\frac{5}{16} - \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Apply the distributive property.

$\frac{6}{5} \cdot \frac{5}{16} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{5} \cdot \frac{5}{16} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Factor $2$ out of $16$ .

$\frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 8} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Cancel the common factor.

$\frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 8} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Rewrite the expression.

$\frac{3}{5} \cdot \frac{5}{8} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5}{8} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Rewrite the expression.

$3 (\frac{1}{8}) + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Combine $3$ and $\frac{1}{8}$ .

$\frac{3}{8} + \frac{6}{5} (- \frac{5 x}{6}) = \frac{6}{5} \cdot 16$

Cancel the common factor of $6$ .

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

$\frac{3}{8} + \frac{6}{5} \cdot \frac{- 5 x}{6} = \frac{6}{5} \cdot 16$

Cancel the common factor.

$\frac{3}{8} + \frac{6}{5} \cdot \frac{- 5 x}{6} = \frac{6}{5} \cdot 16$

Rewrite the expression.

$\frac{3}{8} + \frac{1}{5} (- 5 x) = \frac{6}{5} \cdot 16$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 x$ .

$\frac{3}{8} + \frac{1}{5} (5 (- x)) = \frac{6}{5} \cdot 16$

Cancel the common factor.

$\frac{3}{8} + \frac{1}{5} (5 (- x)) = \frac{6}{5} \cdot 16$

Rewrite the expression.

$\frac{3}{8} - x = \frac{6}{5} \cdot 16$

Simplify the right side.

Multiply $\frac{6}{5} \cdot 16$ .

Combine $\frac{6}{5}$ and $16$ .

$\frac{3}{8} - x = \frac{6 \cdot 16}{5}$

Multiply $6$ by $16$ .

$\frac{3}{8} - x = \frac{96}{5}$

Step 3

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

Subtract $\frac{3}{8}$ from both sides of the equation.

$- x = \frac{96}{5} - \frac{3}{8}$

To write $\frac{96}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- x = \frac{96}{5} \cdot \frac{8}{8} - \frac{3}{8}$

To write $- \frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x = \frac{96}{5} \cdot \frac{8}{8} - \frac{3}{8} \cdot \frac{5}{5}$

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{96}{5}$ by $\frac{8}{8}$ .

$- x = \frac{96 \cdot 8}{5 \cdot 8} - \frac{3}{8} \cdot \frac{5}{5}$

Multiply $5$ by $8$ .

$- x = \frac{96 \cdot 8}{40} - \frac{3}{8} \cdot \frac{5}{5}$

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

$- x = \frac{96 \cdot 8}{40} - \frac{3 \cdot 5}{8 \cdot 5}$

Multiply $8$ by $5$ .

$- x = \frac{96 \cdot 8}{40} - \frac{3 \cdot 5}{40}$

Combine the numerators over the common denominator.

$- x = \frac{96 \cdot 8 - 3 \cdot 5}{40}$

Simplify the numerator.

Multiply $96$ by $8$ .

$- x = \frac{768 - 3 \cdot 5}{40}$

Multiply $- 3$ by $5$ .

$- x = \frac{768 - 15}{40}$

Subtract $15$ from $768$ .

$- x = \frac{753}{40}$

Step 4

Divide each term in $- x = \frac{753}{40}$ by $- 1$ and simplify.

Divide each term in $- x = \frac{753}{40}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{753}{40}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{753}{40}}{- 1}$

Divide $x$ by $1$ .

$x = \frac{\frac{753}{40}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{753}{40}}{- 1}$ .

$x = - 1 \cdot \frac{753}{40}$

Rewrite $- 1 \cdot \frac{753}{40}$ as $- \frac{753}{40}$ .

$x = - \frac{753}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{753}{40}$

Decimal Form:

$x = - 18.825$

Mixed Number Form:

$x = - 18 \frac{33}{40}$

Solve for x 5/6(3/8-x)=16

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