Solve for x 5-1/2x=5/8x+2

$5 - \frac{1}{2} x = \frac{5}{8} x + 2$

Step 1

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

$5 - \frac{x}{2} = \frac{5}{8} x + 2$

Step 2

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

$5 - \frac{x}{2} = \frac{5 x}{8} + 2$

Step 3

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

Subtract $\frac{5 x}{8}$ from both sides of the equation.

$5 - \frac{x}{2} - \frac{5 x}{8} = 2$

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5 - \frac{x}{2} \cdot \frac{4}{4} - \frac{5 x}{8} = 2$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{4}{4}$ .

$5 - \frac{x \cdot 4}{2 \cdot 4} - \frac{5 x}{8} = 2$

Multiply $2$ by $4$ .

$5 - \frac{x \cdot 4}{8} - \frac{5 x}{8} = 2$

Combine the numerators over the common denominator.

$5 + \frac{- x \cdot 4 - 5 x}{8} = 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x \cdot 4 - 5 x$ .

Factor $x$ out of $- x \cdot 4$ .

$5 + \frac{x (- 1 \cdot 4) - 5 x}{8} = 2$

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

$5 + \frac{x (- 1 \cdot 4) + x \cdot - 5}{8} = 2$

Factor $x$ out of $x (- 1 \cdot 4) + x \cdot - 5$ .

$5 + \frac{x (- 1 \cdot 4 - 5)}{8} = 2$

Multiply $- 1$ by $4$ .

$5 + \frac{x (- 4 - 5)}{8} = 2$

Subtract $5$ from $- 4$ .

$5 + \frac{x \cdot - 9}{8} = 2$

Move $- 9$ to the left of $x$ .

$5 + \frac{- 9 \cdot x}{8} = 2$

Move the negative in front of the fraction.

$5 - \frac{9 x}{8} = 2$

Step 4

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

Subtract $5$ from both sides of the equation.

$- \frac{9 x}{8} = 2 - 5$

Subtract $5$ from $2$ .

$- \frac{9 x}{8} = - 3$

Step 5

Multiply both sides of the equation by $- \frac{8}{9}$ .

$- \frac{8}{9} (- \frac{9 x}{8}) = - \frac{8}{9} \cdot - 3$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{8}{9} (- \frac{9 x}{8})$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{8}{9}$ into the numerator.

$\frac{- 8}{9} (- \frac{9 x}{8}) = - \frac{8}{9} \cdot - 3$

Move the leading negative in $- \frac{9 x}{8}$ into the numerator.

$\frac{- 8}{9} \cdot \frac{- 9 x}{8} = - \frac{8}{9} \cdot - 3$

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{9} \cdot \frac{- 9 x}{8} = - \frac{8}{9} \cdot - 3$

Cancel the common factor.

$\frac{8 \cdot - 1}{9} \cdot \frac{- 9 x}{8} = - \frac{8}{9} \cdot - 3$

Rewrite the expression.

$\frac{- 1}{9} (- 9 x) = - \frac{8}{9} \cdot - 3$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 x$ .

$\frac{- 1}{9} (9 (- x)) = - \frac{8}{9} \cdot - 3$

Cancel the common factor.

$\frac{- 1}{9} (9 (- x)) = - \frac{8}{9} \cdot - 3$

Rewrite the expression.

$- - x = - \frac{8}{9} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{8}{9} \cdot - 3$

Multiply $x$ by $1$ .

$x = - \frac{8}{9} \cdot - 3$

Simplify the right side.

Simplify $- \frac{8}{9} \cdot - 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{8}{9}$ into the numerator.

$x = \frac{- 8}{9} \cdot - 3$

Factor $3$ out of $9$ .

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $- 8$ by $- 1$ .

$x = \frac{8}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{3}$

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

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

Solve for x 5-1/2x=5/8x+2

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