Pre-Algebra Examples

$4 (x - 1) = \frac{1}{2} \cdot (x - 8)$

Step 1

Simplify $4 (x - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 (x - 1) = \frac{1}{2} \cdot (x - 8)$

Step 1.2

Simplify by adding zeros.

$4 (x - 1) = \frac{1}{2} \cdot (x - 8)$

Step 1.3

Apply the distributive property.

$4 x + 4 \cdot - 1 = \frac{1}{2} \cdot (x - 8)$

Step 1.4

Multiply $4$ by $- 1$ .

$4 x - 4 = \frac{1}{2} \cdot (x - 8)$

Step 2

Simplify $\frac{1}{2} \cdot (x - 8)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $- 8$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

Combine $4 x$ and $\frac{2}{2}$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $4 x \cdot 2 - x$ .

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Step 3.5.1.1.1

Factor $x$ out of $4 x \cdot 2$ .

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

Step 3.5.1.1.2

Factor $x$ out of $- x$ .

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

Step 3.5.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 1$ .

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

Step 3.5.1.2

Multiply $4$ by $2$ .

$\frac{x (8 - 1)}{2} - 4 = - 4$

Step 3.5.1.3

Subtract $1$ from $8$ .

$\frac{x \cdot 7}{2} - 4 = - 4$

Step 3.5.2

Move $7$ to the left of $x$ .

$\frac{7 x}{2} - 4 = - 4$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$\frac{7 x}{2} = - 4 + 4$

Step 4.2

Add $- 4$ and $4$ .

$\frac{7 x}{2} = 0$

Step 5

Set the numerator equal to zero.

$7 x = 0$

Step 6

Divide each term in $7 x = 0$ by $7$ and simplify.

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Step 6.1

Divide each term in $7 x = 0$ by $7$ .

$\frac{7 x}{7} = \frac{0}{7}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{0}{7}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{7}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $0$ by $7$ .

$x = 0$