Algebra Examples

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

Step 1

Simplify $x + \frac{x}{3}$ .

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move $3$ to the left of $x$ .

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

Step 1.3.2

Add $3 x$ and $x$ .

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

Step 2

Multiply both sides of the equation by $\frac{3}{4}$ .

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

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

Simplify $\frac{3}{4} \cdot \frac{4 x}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

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

Step 3.1.1.1.2

Rewrite the expression.

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

Step 3.1.1.2

Cancel the common factor of $4$ .

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Step 3.1.1.2.1

Factor $4$ out of $4 x$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$x = 3$