Pre-Algebra Examples

$2 (x + 2) = \frac{3}{4} x - 1$

Step 1

Simplify $2 (x + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (x + 2) = \frac{3}{4} x - 1$

Step 1.2

Simplify by adding zeros.

$2 (x + 2) = \frac{3}{4} x - 1$

Step 1.3

Apply the distributive property.

$2 x + 2 \cdot 2 = \frac{3}{4} x - 1$

Step 1.4

Multiply $2$ by $2$ .

$2 x + 4 = \frac{3}{4} x - 1$

Step 2

Combine $\frac{3}{4}$ and $x$ .

$2 x + 4 = \frac{3 x}{4} - 1$

Step 3

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

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Step 3.1

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$2 x + 4 - \frac{3 x}{4} = - 1$

Step 3.2

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

$2 x \cdot \frac{4}{4} - \frac{3 x}{4} + 4 = - 1$

Step 3.3

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

$\frac{2 x \cdot 4}{4} - \frac{3 x}{4} + 4 = - 1$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 4 - 3 x}{4} + 4 = - 1$

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 $2 x \cdot 4 - 3 x$ .

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Step 3.5.1.1.1

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

$\frac{x (2 \cdot 4) - 3 x}{4} + 4 = - 1$

Step 3.5.1.1.2

Factor $x$ out of $- 3 x$ .

$\frac{x (2 \cdot 4) + x \cdot - 3}{4} + 4 = - 1$

Step 3.5.1.1.3

Factor $x$ out of $x (2 \cdot 4) + x \cdot - 3$ .

$\frac{x (2 \cdot 4 - 3)}{4} + 4 = - 1$

Step 3.5.1.2

Multiply $2$ by $4$ .

$\frac{x (8 - 3)}{4} + 4 = - 1$

Step 3.5.1.3

Subtract $3$ from $8$ .

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

Step 3.5.2

Move $5$ to the left of $x$ .

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

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

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

Step 4.2

Subtract $4$ from $- 1$ .

$\frac{5 x}{4} = - 5$

Step 5

Multiply both sides of the equation by $\frac{4}{5}$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $5$ .

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Step 6.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{4}{5} \cdot - 5$ .

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Step 6.2.1.1

Cancel the common factor of $5$ .

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Step 6.2.1.1.1

Factor $5$ out of $- 5$ .

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

Step 6.2.1.1.2

Cancel the common factor.

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

Step 6.2.1.1.3

Rewrite the expression.

$x = 4 \cdot - 1$

Step 6.2.1.2

Multiply $4$ by $- 1$ .

$x = - 4$