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

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

Rewrite the equation as $- 2 x - (2 x - 4) - \frac{1}{2} = \frac{5}{2}$ .

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

Simplify $- 2 x - (2 x - 4) - \frac{1}{2}$ .

Find the common denominator.

Write $- 2 x$ as a fraction with denominator $1$ .

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

Multiply $\frac{- 2 x}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{- 2 x}{1}$ by $\frac{2}{2}$ .

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

Write $- (2 x - 4)$ as a fraction with denominator $1$ .

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

Multiply $\frac{- (2 x - 4)}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{- (2 x - 4)}{1}$ by $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $2$ by $- 2$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $- 4$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 2$ .

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

Multiply $4$ by $2$ .

$\frac{- 4 x - 4 x + 8 - 1}{2} = \frac{5}{2}$

Simplify terms.

Subtract $4 x$ from $- 4 x$ .

$\frac{- 8 x + 8 - 1}{2} = \frac{5}{2}$

Subtract $1$ from $8$ .

$\frac{- 8 x + 7}{2} = \frac{5}{2}$

Factor $- 1$ out of $- 8 x$ .

$\frac{- (8 x) + 7}{2} = \frac{5}{2}$

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{- (8 x) - 1 (- 7)}{2} = \frac{5}{2}$

Factor $- 1$ out of $- (8 x) - 1 (- 7)$ .

$\frac{- (8 x - 7)}{2} = \frac{5}{2}$

Simplify the expression.

Rewrite $- (8 x - 7)$ as $- 1 (8 x - 7)$ .

$\frac{- 1 (8 x - 7)}{2} = \frac{5}{2}$

Move the negative in front of the fraction.

$- \frac{8 x - 7}{2} = \frac{5}{2}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (8 x - 7) = 5$

Simplify $- (8 x - 7)$ .

Apply the distributive property.

$- (8 x) - - 7 = 5$

Multiply.

Multiply $8$ by $- 1$ .

$- 8 x - - 7 = 5$

Multiply $- 1$ by $- 7$ .

$- 8 x + 7 = 5$

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

Subtract $7$ from both sides of the equation.

$- 8 x = 5 - 7$

Subtract $7$ from $5$ .

$- 8 x = - 2$

Divide each term in $- 8 x = - 2$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 2$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 2}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 2}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 8}$

Simplify the right side.

Cancel the common factor of $- 2$ and $- 8$ .

Factor $- 2$ out of $- 2$ .

$x = \frac{- 2 (1)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.25$

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

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