Algebra Examples

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

Step 1

Multiply $x + 5$ by $\frac{2}{3}$ .

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

Step 2

Multiply each term in $(x + 5) (\frac{2}{3}) = 4$ by $\frac{3}{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $(x + 5) (\frac{2}{3}) = 4$ by $\frac{3}{2}$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

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

$(\frac{x \cdot 2}{3} + 5 (\frac{2}{3})) \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.3

Multiply $5 (\frac{2}{3})$ .

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Step 2.2.3.1

Combine $5$ and $\frac{2}{3}$ .

$(\frac{x \cdot 2}{3} + \frac{5 \cdot 2}{3}) \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.3.2

Multiply $5$ by $2$ .

$(\frac{x \cdot 2}{3} + \frac{10}{3}) \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.4

Move $2$ to the left of $x$ .

$(\frac{2 x}{3} + \frac{10}{3}) \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5

Simplify terms.

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Step 2.2.5.1

Apply the distributive property.

$\frac{2 x}{3} \cdot \frac{3}{2} + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.2

Cancel the common factor of $2$ .

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Step 2.2.5.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{3} \cdot \frac{3}{2} + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.2.2

Cancel the common factor.

$\frac{2 x}{3} \cdot \frac{3}{2} + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.2.3

Rewrite the expression.

$\frac{x}{3} \cdot 3 + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.3

Cancel the common factor of $3$ .

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Step 2.2.5.3.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.3.2

Rewrite the expression.

$x + \frac{10}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.4

Cancel the common factor of $2$ .

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Step 2.2.5.4.1

Factor $2$ out of $10$ .

$x + \frac{2 (5)}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.4.2

Cancel the common factor.

$x + \frac{2 \cdot 5}{3} \cdot \frac{3}{2} = 4 (\frac{3}{2})$

Step 2.2.5.4.3

Rewrite the expression.

$x + \frac{5}{3} \cdot 3 = 4 (\frac{3}{2})$

Step 2.2.5.5

Cancel the common factor of $3$ .

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Step 2.2.5.5.1

Cancel the common factor.

$x + \frac{5}{3} \cdot 3 = 4 (\frac{3}{2})$

Step 2.2.5.5.2

Rewrite the expression.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Factor $2$ out of $4$ .

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

Step 2.3.1.2

Cancel the common factor.

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

Step 2.3.1.3

Rewrite the expression.

$x + 5 = 2 \cdot 3$

Step 2.3.2

Multiply $2$ by $3$ .

$x + 5 = 6$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$x = 6 - 5$

Step 3.2

Subtract $5$ from $6$ .

$x = 1$