Solve for x 1/4x+x=-3+1/2x

$\frac{1}{4} x + x = - 3 + \frac{1}{2} x$

Simplify $\frac{1}{4} x + x$ .

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

$\frac{x}{4} + x = - 3 + \frac{1}{2} x$

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $4$ to the left of $x$ .

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

Add $x$ and $4 x$ .

$\frac{5 x}{4} = - 3 + \frac{1}{2} x$

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

$\frac{5 x}{4} = - 3 + \frac{x}{2}$

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

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

$\frac{5 x}{4} - \frac{x}{2} = - 3$

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

$\frac{5 x}{4} - \frac{x}{2} \cdot \frac{2}{2} = - 3$

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

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

$\frac{5 x}{4} - \frac{x \cdot 2}{2 \cdot 2} = - 3$

Multiply $2$ by $2$ .

$\frac{5 x}{4} - \frac{x \cdot 2}{4} = - 3$

Combine the numerators over the common denominator.

$\frac{5 x - x \cdot 2}{4} = - 3$

Simplify the numerator.

Factor $x$ out of $5 x - x \cdot 2$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - x \cdot 2}{4} = - 3$

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

$\frac{x \cdot 5 + x (- 1 \cdot 2)}{4} = - 3$

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 2)$ .

$\frac{x (5 - 1 \cdot 2)}{4} = - 3$

Multiply $- 1$ by $2$ .

$\frac{x (5 - 2)}{4} = - 3$

Subtract $2$ from $5$ .

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

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

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

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

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$x = - 4$

Solve for x 1/4x+x=-3+1/2x

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