Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Find the common denominator.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

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

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

Step 2.1.6

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $2$ by $- 2$ .

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

Step 2.3.2

Apply the distributive property.

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

Step 2.3.3

Multiply $2$ by $- 1$ .

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

Step 2.3.4

Multiply $- 1$ by $- 4$ .

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

Step 2.3.5

Apply the distributive property.

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

Step 2.3.6

Multiply $2$ by $- 2$ .

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

Step 2.3.7

Multiply $4$ by $2$ .

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

Step 2.4

Simplify terms.

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Step 2.4.1

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

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

Step 2.4.2

Subtract $1$ from $8$ .

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

Step 2.4.3

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

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

Step 2.4.4

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

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

Step 2.4.5

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

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

Step 2.4.6

Simplify the expression.

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Step 2.4.6.1

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

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

Step 2.4.6.2

Move the negative in front of the fraction.

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

Step 3

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

$- (8 x - 7) = 5$

Step 4

Simplify $- (8 x - 7)$ .

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply.

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Step 4.2.1

Multiply $8$ by $- 1$ .

$- 8 x - - 7 = 5$

Step 4.2.2

Multiply $- 1$ by $- 7$ .

$- 8 x + 7 = 5$

Step 5

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

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Step 5.1

Subtract $7$ from both sides of the equation.

$- 8 x = 5 - 7$

Step 5.2

Subtract $7$ from $5$ .

$- 8 x = - 2$

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 8$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

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

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Step 6.3.1.1

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

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

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

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

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

Step 6.3.1.2.2

Cancel the common factor.

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

Step 6.3.1.2.3

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.25$