Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

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

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

Step 1.5.2

Factor $2$ out of $4$ .

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

Step 1.5.3

Cancel the common factor.

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

Step 1.5.4

Rewrite the expression.

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

Step 1.6

Multiply $- 1$ by $2$ .

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

Step 2

Simplify $\frac{3}{4} \cdot (x - 4)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Factor $4$ out of $- 4$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 2.4

Multiply $3$ by $- 1$ .

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

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.

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

Step 3.2

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

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

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

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 $- x \cdot 2 - 3 x$ .

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Step 3.5.1.1.1

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

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

Step 3.5.1.1.2

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

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

Step 3.5.1.1.3

Factor $x$ out of $x (- 1 \cdot 2) + x \cdot - 3$ .

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

Step 3.5.1.2

Multiply $- 1$ by $2$ .

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

Step 3.5.1.3

Subtract $3$ from $- 2$ .

$\frac{x \cdot - 5}{4} - 2 = - 3$

Step 3.5.2

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

$\frac{- 5 \cdot x}{4} - 2 = - 3$

Step 3.5.3

Move the negative in front of the fraction.

$- \frac{5 x}{4} - 2 = - 3$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$- \frac{5 x}{4} = - 3 + 2$

Step 4.2

Add $- 3$ and $2$ .

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

Step 5

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

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

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 $- \frac{4}{5} (- \frac{5 x}{4})$ .

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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

Move the leading negative in $- \frac{4}{5}$ into the numerator.

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

Step 6.1.1.1.2

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

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

Step 6.1.1.1.3

Factor $4$ out of $- 4$ .

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

Step 6.1.1.1.4

Cancel the common factor.

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

Step 6.1.1.1.5

Rewrite the expression.

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

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 $- 5 x$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 6.1.1.3.2

Multiply $x$ by $1$ .

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- \frac{4}{5} \cdot - 1$ .

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Step 6.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 6.2.1.2

Multiply $\frac{4}{5}$ by $1$ .

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.8$