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

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

Step 1

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

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

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

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

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

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

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

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $1$ .

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

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

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

Move the negative in front of the fraction.

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

Step 2

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

Add $\frac{3}{2}$ to both sides of the equation.

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $2$ and $3$ .

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

Step 3

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

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

Step 4

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.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- 4 (\frac{5}{2})$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$x = - 10$

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

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