Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Cancel the common factor of $2$ .

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Step 2.1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.1.2.2

Factor $2$ out of $2 x$ .

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

Step 2.1.2.3

Cancel the common factor.

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

Step 2.1.2.4

Rewrite the expression.

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

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.1.3.2

Factor $2$ out of $- 4$ .

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

Step 2.1.3.3

Cancel the common factor.

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

Step 2.1.3.4

Rewrite the expression.

$- 1 x - 1 \cdot - 2 - 2 x = 5$

Step 2.1.4

Multiply $- 1$ by $- 2$ .

$- 1 x + 2 - 2 x = 5$

Step 2.1.5

Rewrite $- 1 x$ as $- x$ .

$- x + 2 - 2 x = 5$

Step 2.2

Subtract $2 x$ from $- x$ .

$- 3 x + 2 = 5$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$- 3 x = 5 - 2$

Step 3.2

Subtract $2$ from $5$ .

$- 3 x = 3$

Step 4

Divide each term in $- 3 x = 3$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 x = 3$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{3}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{3}{- 3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $3$ by $- 3$ .

$x = - 1$