Solve for x (5x)/4+1/2=x-1/2

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

Step 1

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - x \cdot 4$ .

Factor $x$ out of $5 x$ .

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

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

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

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 4)$ .

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

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $5$ .

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

Multiply $x$ by $1$ .

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

Step 2

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

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $- 1$ .

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

Divide $- 2$ by $2$ .

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

Step 3

Multiply both sides of the equation by $4$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 4 \cdot - 1$

Simplify the right side.

Multiply $4$ by $- 1$ .

$x = - 4$

Solve for x (5x)/4+1/2=x-1/2

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