Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

$5 - x = 0 + 0 + \frac{1}{2} \cdot (4 - x)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

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

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

Step 2

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

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Step 2.1

Add $\frac{x}{2}$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

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

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Step 2.5.1.1.1

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

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

Step 2.5.1.1.2

Raise $x$ to the power of $1$ .

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

Step 2.5.1.1.3

Factor $x$ out of $x^{1}$ .

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

Step 2.5.1.1.4

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

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

Step 2.5.1.2

Multiply $- 1$ by $2$ .

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

Step 2.5.1.3

Add $- 2$ and $1$ .

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

Step 2.5.2

Move $- 1$ to the left of $x$ .

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

Step 2.5.3

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

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

Step 3.2

Subtract $5$ from $2$ .

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

Step 4

Multiply both sides of the equation by $- 2$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

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

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

Step 5.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 5.1.1.1.3

Cancel the common factor.

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

Step 5.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 3$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 3$

Step 5.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 2$ by $- 3$ .

$x = 6$