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

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

Step 1

Simplify each term.

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

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

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

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

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

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

Factor $x$ out of $x \cdot - 3 + x (- 1 \cdot 2)$ .

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

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 3$ .

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

Move $- 5$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Step 4

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

Subtract $2$ from both sides of the equation.

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

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

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

Combine $- 2$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $- 1$ .

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

Move the negative in front of the fraction.

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

Step 5

Multiply both sides of the equation by $- \frac{4}{5}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

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

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

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

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x = 2$

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

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