Algebra Examples

$\frac{4}{3} x + \frac{2}{3} x = \frac{1}{3} x + 5$

Step 1

Simplify $\frac{4}{3} x + \frac{2}{3} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{4 x}{3} + \frac{2}{3} x = \frac{1}{3} x + 5$

Step 1.1.2

Combine $\frac{2}{3}$ and $x$ .

$\frac{4 x}{3} + \frac{2 x}{3} = \frac{1}{3} x + 5$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{4 x + 2 x}{3} = \frac{1}{3} x + 5$

Step 1.2.2

Add $4 x$ and $2 x$ .

$\frac{6 x}{3} = \frac{1}{3} x + 5$

Step 1.2.3

Cancel the common factor of $6$ and $3$ .

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Step 1.2.3.1

Factor $3$ out of $6 x$ .

$\frac{3 (2 x)}{3} = \frac{1}{3} x + 5$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 x)}{3 (1)} = \frac{1}{3} x + 5$

Step 1.2.3.2.2

Cancel the common factor.

$\frac{3 (2 x)}{3 \cdot 1} = \frac{1}{3} x + 5$

Step 1.2.3.2.3

Rewrite the expression.

$\frac{2 x}{1} = \frac{1}{3} x + 5$

Step 1.2.3.2.4

Divide $2 x$ by $1$ .

$2 x = \frac{1}{3} x + 5$

Step 2

Combine $\frac{1}{3}$ and $x$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

Combine $2 x$ and $\frac{3}{3}$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $x$ out of $2 x \cdot 3 - x$ .

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Step 3.5.1.1

Factor $x$ out of $2 x \cdot 3$ .

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

Step 3.5.1.2

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 3) + x \cdot - 1}{3} = 5$

Step 3.5.1.3

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

$\frac{x (2 \cdot 3 - 1)}{3} = 5$

Step 3.5.2

Multiply $2$ by $3$ .

$\frac{x (6 - 1)}{3} = 5$

Step 3.5.3

Subtract $1$ from $6$ .

$\frac{x \cdot 5}{3} = 5$

Step 3.6

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

$\frac{5 x}{3} = 5$

Step 4

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot 5$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{3}{5} \cdot \frac{5 x}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot 5$

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{5} \cdot 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$x = \frac{3}{5} \cdot 5$

Step 5.2.1.2

Rewrite the expression.

$x = 3$