Solve for x 1/4x-1/8=7/8+1/2x

$\frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x$

Step 2

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

$\frac{x}{4} - \frac{1}{8} = \frac{7}{8} + \frac{x}{2}$

Step 3

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{x}{4} - \frac{1}{8} - \frac{x}{2} = \frac{7}{8}$

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

$\frac{x}{4} - \frac{x}{2} \cdot \frac{2}{2} - \frac{1}{8} = \frac{7}{8}$

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

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

$\frac{x}{4} - \frac{x \cdot 2}{2 \cdot 2} - \frac{1}{8} = \frac{7}{8}$

Multiply $2$ by $2$ .

$\frac{x}{4} - \frac{x \cdot 2}{4} - \frac{1}{8} = \frac{7}{8}$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{4} - \frac{1}{8} = \frac{7}{8}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - x \cdot 2$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{4} - \frac{1}{8} = \frac{7}{8}$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{4} - \frac{1}{8} = \frac{7}{8}$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{4} - \frac{1}{8} = \frac{7}{8}$

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 2)$ .

$\frac{x (1 - 1 \cdot 2)}{4} - \frac{1}{8} = \frac{7}{8}$

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{4} - \frac{1}{8} = \frac{7}{8}$

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{4} - \frac{1}{8} = \frac{7}{8}$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{4} - \frac{1}{8} = \frac{7}{8}$

Move the negative in front of the fraction.

$- \frac{x}{4} - \frac{1}{8} = \frac{7}{8}$

Step 4

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

Add $\frac{1}{8}$ to both sides of the equation.

$- \frac{x}{4} = \frac{7}{8} + \frac{1}{8}$

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{7 + 1}{8}$

Add $7$ and $1$ .

$- \frac{x}{4} = \frac{8}{8}$

Divide $8$ by $8$ .

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

Step 5

Multiply both sides of the equation by $- 4$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{x}{4})$ .

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 4 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 \cdot 1$

Multiply $x$ by $1$ .

$x = - 4 \cdot 1$

Simplify the right side.

Multiply $- 4$ by $1$ .

$x = - 4$

Solve for x 1/4x-1/8=7/8+1/2x

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