Algebra Examples

$\frac{3}{4} \cdot (x - 4) + \frac{1}{4} x = 5$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{3}{4} x + \frac{3}{4} \cdot - 4 + \frac{1}{4} x = 5$

Step 1.1.2

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

$\frac{3 x}{4} + \frac{3}{4} \cdot - 4 + \frac{1}{4} x = 5$

Step 1.1.3

Cancel the common factor of $4$ .

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Step 1.1.3.1

Factor $4$ out of $- 4$ .

$\frac{3 x}{4} + \frac{3}{4} \cdot (4 (- 1)) + \frac{1}{4} x = 5$

Step 1.1.3.2

Cancel the common factor.

$\frac{3 x}{4} + \frac{3}{4} \cdot (4 \cdot - 1) + \frac{1}{4} x = 5$

Step 1.1.3.3

Rewrite the expression.

$\frac{3 x}{4} + 3 \cdot - 1 + \frac{1}{4} x = 5$

Step 1.1.4

Multiply $3$ by $- 1$ .

$\frac{3 x}{4} - 3 + \frac{1}{4} x = 5$

Step 1.1.5

Combine $\frac{1}{4}$ and $x$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

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

Step 1.2.2

Add $3 x$ and $x$ .

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

Step 1.2.3

Cancel the common factor of $4$ .

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Step 1.2.3.1

Cancel the common factor.

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

Step 1.2.3.2

Divide $x$ by $1$ .

$- 3 + x = 5$

Step 2

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

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Step 2.1

Add $3$ to both sides of the equation.

$x = 5 + 3$

Step 2.2

Add $5$ and $3$ .

$x = 8$