Solve for x 1/4x+18=x

$\frac{1}{4} x + 18 = x$

Step 1

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

$\frac{x}{4} + 18 = x$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{x}{4} + 18 - x = 0$

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

$\frac{x}{4} - x \cdot \frac{4}{4} + 18 = 0$

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

$\frac{x}{4} + \frac{- x \cdot 4}{4} + 18 = 0$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 4}{4} + 18 = 0$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x^{1} - x \cdot 4}{4} + 18 = 0$

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

$\frac{x \cdot 1 - x \cdot 4}{4} + 18 = 0$

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

$\frac{x \cdot 1 + x (- 1 \cdot 4)}{4} + 18 = 0$

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

$\frac{x (1 - 1 \cdot 4)}{4} + 18 = 0$

Multiply $- 1$ by $4$ .

$\frac{x (1 - 4)}{4} + 18 = 0$

Subtract $4$ from $1$ .

$\frac{x \cdot - 3}{4} + 18 = 0$

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{4} + 18 = 0$

Move the negative in front of the fraction.

$- \frac{3 x}{4} + 18 = 0$

Step 3

Subtract $18$ from both sides of the equation.

$- \frac{3 x}{4} = - 18$

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 18$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 18$

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 18$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 18$

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 18$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} \cdot - 18$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 18$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 18$

Rewrite the expression.

$- - x = - \frac{4}{3} \cdot - 18$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} \cdot - 18$

Multiply $x$ by $1$ .

$x = - \frac{4}{3} \cdot - 18$

Simplify the right side.

Simplify $- \frac{4}{3} \cdot - 18$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = \frac{- 4}{3} \cdot - 18$

Factor $3$ out of $- 18$ .

$x = \frac{- 4}{3} \cdot (3 (- 6))$

Cancel the common factor.

$x = \frac{- 4}{3} \cdot (3 \cdot - 6)$

Rewrite the expression.

$x = - 4 \cdot - 6$

Multiply $- 4$ by $- 6$ .

$x = 24$

Solve for x 1/4x+18=x

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