Solve for x 3/4x-7/8x=1

$\frac{3}{4} x - \frac{7}{8} x = 1$

Step 1

Simplify $\frac{3}{4} x - \frac{7}{8} x$ .

Simplify each term.

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} - \frac{7}{8} x = 1$

Combine $x$ and $\frac{7}{8}$ .

$\frac{3 x}{4} - \frac{x \cdot 7}{8} = 1$

Move $7$ to the left of $x$ .

$\frac{3 x}{4} - \frac{7 x}{8} = 1$

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} \cdot \frac{2}{2} - \frac{7 x}{8} = 1$

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

Multiply $\frac{3 x}{4}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2}{4 \cdot 2} - \frac{7 x}{8} = 1$

Multiply $4$ by $2$ .

$\frac{3 x \cdot 2}{8} - \frac{7 x}{8} = 1$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - 7 x}{8} = 1$

Simplify the numerator.

Factor $x$ out of $3 x \cdot 2 - 7 x$ .

Factor $x$ out of $3 x \cdot 2$ .

$\frac{x (3 \cdot 2) - 7 x}{8} = 1$

Factor $x$ out of $- 7 x$ .

$\frac{x (3 \cdot 2) + x \cdot - 7}{8} = 1$

Factor $x$ out of $x (3 \cdot 2) + x \cdot - 7$ .

$\frac{x (3 \cdot 2 - 7)}{8} = 1$

Multiply $3$ by $2$ .

$\frac{x (6 - 7)}{8} = 1$

Subtract $7$ from $6$ .

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- 8$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $8$ .

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

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

Factor $8$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 8 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 8 \cdot 1$

Multiply $x$ by $1$ .

$x = - 8 \cdot 1$

Simplify the right side.

Multiply $- 8$ by $1$ .

$x = - 8$

Solve for x 3/4x-7/8x=1

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