Solve for x 3/4x+5/8=4x

$\frac{3}{4} x + \frac{5}{8} = 4 x$

Step 1

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

$\frac{3 x}{4} + \frac{5}{8} = 4 x$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$\frac{3 x}{4} + \frac{5}{8} - 4 x = 0$

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

$\frac{3 x}{4} - 4 x \cdot \frac{4}{4} + \frac{5}{8} = 0$

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

$\frac{3 x}{4} + \frac{- 4 x \cdot 4}{4} + \frac{5}{8} = 0$

Combine the numerators over the common denominator.

$\frac{3 x - 4 x \cdot 4}{4} + \frac{5}{8} = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - 4 x \cdot 4$ .

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - 4 x \cdot 4}{4} + \frac{5}{8} = 0$

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

$\frac{x \cdot 3 + x (- 4 \cdot 4)}{4} + \frac{5}{8} = 0$

Factor $x$ out of $x \cdot 3 + x (- 4 \cdot 4)$ .

$\frac{x (3 - 4 \cdot 4)}{4} + \frac{5}{8} = 0$

Multiply $- 4$ by $4$ .

$\frac{x (3 - 16)}{4} + \frac{5}{8} = 0$

Subtract $16$ from $3$ .

$\frac{x \cdot - 13}{4} + \frac{5}{8} = 0$

Move $- 13$ to the left of $x$ .

$\frac{- 13 \cdot x}{4} + \frac{5}{8} = 0$

Move the negative in front of the fraction.

$- \frac{13 x}{4} + \frac{5}{8} = 0$

Step 3

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

$- \frac{13 x}{4} = - \frac{5}{8}$

Step 4

Multiply both sides of the equation by $- \frac{4}{13}$ .

$- \frac{4}{13} (- \frac{13 x}{4}) = - \frac{4}{13} (- \frac{5}{8})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{13} (- \frac{13 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{13}$ into the numerator.

$\frac{- 4}{13} (- \frac{13 x}{4}) = - \frac{4}{13} (- \frac{5}{8})$

Move the leading negative in $- \frac{13 x}{4}$ into the numerator.

$\frac{- 4}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} (- \frac{5}{8})$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} (- \frac{5}{8})$

Cancel the common factor.

$\frac{4 \cdot - 1}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} (- \frac{5}{8})$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{4}{13} (- \frac{5}{8})$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{4}{13} (- \frac{5}{8})$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{4}{13} (- \frac{5}{8})$

Rewrite the expression.

$- - x = - \frac{4}{13} (- \frac{5}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{13} (- \frac{5}{8})$

Multiply $x$ by $1$ .

$x = - \frac{4}{13} (- \frac{5}{8})$

Simplify the right side.

Simplify $- \frac{4}{13} (- \frac{5}{8})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{13}$ into the numerator.

$x = \frac{- 4}{13} (- \frac{5}{8})$

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$x = \frac{- 4}{13} \cdot \frac{- 5}{8}$

Factor $4$ out of $- 4$ .

$x = \frac{4 (- 1)}{13} \cdot \frac{- 5}{8}$

Factor $4$ out of $8$ .

$x = \frac{4 \cdot - 1}{13} \cdot \frac{- 5}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{4 \cdot - 1}{13} \cdot \frac{- 5}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{13} \cdot \frac{- 5}{2}$

Multiply $\frac{- 1}{13}$ by $\frac{- 5}{2}$ .

$x = \frac{- - 5}{13 \cdot 2}$

Multiply.

Multiply $- 1$ by $- 5$ .

$x = \frac{5}{13 \cdot 2}$

Multiply $13$ by $2$ .

$x = \frac{5}{26}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{26}$

Decimal Form:

$x = 0.1\overline{923076}$

Solve for x 3/4x+5/8=4x

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