Algebra Examples

$\frac{1}{2} \cdot (2 x + 2) - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 2 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot 2 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 2 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.2.3

Rewrite the expression.

$x + \frac{1}{2} \cdot 2 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Cancel the common factor.

$x + \frac{1}{2} \cdot 2 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.3.2

Rewrite the expression.

$x + 1 - \frac{1}{4} \cdot (3 x - 1) = 15$

Step 1.1.4

Apply the distributive property.

$x + 1 - \frac{1}{4} (3 x) - \frac{1}{4} \cdot - 1 = 15$

Step 1.1.5

Multiply $- \frac{1}{4} (3 x)$ .

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Step 1.1.5.1

Multiply $3$ by $- 1$ .

$x + 1 - 3 (\frac{1}{4}) x - \frac{1}{4} \cdot - 1 = 15$

Step 1.1.5.2

Combine $- 3$ and $\frac{1}{4}$ .

$x + 1 + \frac{- 3}{4} x - \frac{1}{4} \cdot - 1 = 15$

Step 1.1.5.3

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

$x + 1 + \frac{- 3 x}{4} - \frac{1}{4} \cdot - 1 = 15$

Step 1.1.6

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

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Step 1.1.6.1

Multiply $- 1$ by $- 1$ .

$x + 1 + \frac{- 3 x}{4} + 1 (\frac{1}{4}) = 15$

Step 1.1.6.2

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

$x + 1 + \frac{- 3 x}{4} + \frac{1}{4} = 15$

Step 1.1.7

Move the negative in front of the fraction.

$x + 1 - \frac{3 x}{4} + \frac{1}{4} = 15$

Step 1.2

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

$x \cdot \frac{4}{4} - \frac{3 x}{4} + 1 + \frac{1}{4} = 15$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{x \cdot 4}{4} - \frac{3 x}{4} + 1 + \frac{1}{4} = 15$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x}{4} + 1 + \frac{1}{4} = 15$

Step 1.3.3

Combine the numerators over the common denominator.

$1 + \frac{x \cdot 4 - 3 x + 1}{4} = 15$

Step 1.4

Move $4$ to the left of $x$ .

$1 + \frac{4 x - 3 x + 1}{4} = 15$

Step 1.5

Simplify terms.

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Step 1.5.1

Subtract $3 x$ from $4 x$ .

$1 + \frac{x + 1}{4} = 15$

Step 1.5.2

Write $1$ as a fraction with a common denominator.

$\frac{4}{4} + \frac{x + 1}{4} = 15$

Step 1.5.3

Combine the numerators over the common denominator.

$\frac{4 + x + 1}{4} = 15$

Step 1.5.4

Add $4$ and $1$ .

$\frac{x + 5}{4} = 15$

Step 2

Multiply both sides of the equation by $4$ .

$4 \frac{x + 5}{4} = 4 \cdot 15$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$4 \frac{x + 5}{4} = 4 \cdot 15$

Step 3.1.1.2

Rewrite the expression.

$x + 5 = 4 \cdot 15$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $4$ by $15$ .

$x + 5 = 60$

Step 4

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

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Step 4.1

Subtract $5$ from both sides of the equation.

$x = 60 - 5$

Step 4.2

Subtract $5$ from $60$ .

$x = 55$