Algebra Examples

$\frac{2}{3} (3 x + 6) = 14$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (3 x + 6)) = \frac{3}{2} \cdot 14$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (3 x + 6))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} (3 x) + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 14$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{3}{2} (\frac{2}{3} (3 (x)) + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 14$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} (3 x) + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 14$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{3}{2} (2 x + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 14$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $6$ .

$\frac{3}{2} (2 x + \frac{2}{3} \cdot (3 (2))) = \frac{3}{2} \cdot 14$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{3}{2} (2 x + \frac{2}{3} \cdot (3 \cdot 2)) = \frac{3}{2} \cdot 14$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{3}{2} (2 x + 2 \cdot 2) = \frac{3}{2} \cdot 14$

Step 2.1.1.4

Multiply $2$ by $2$ .

$\frac{3}{2} (2 x + 4) = \frac{3}{2} \cdot 14$

Step 2.1.1.5

Apply the distributive property.

$\frac{3}{2} (2 x) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 14$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $2 x$ .

$\frac{3}{2} (2 (x)) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 14$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{3}{2} (2 x) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 14$

Step 2.1.1.6.3

Rewrite the expression.

$3 x + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 14$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $4$ .

$3 x + \frac{3}{2} \cdot (2 (2)) = \frac{3}{2} \cdot 14$

Step 2.1.1.7.2

Cancel the common factor.

$3 x + \frac{3}{2} \cdot (2 \cdot 2) = \frac{3}{2} \cdot 14$

Step 2.1.1.7.3

Rewrite the expression.

$3 x + 3 \cdot 2 = \frac{3}{2} \cdot 14$

Step 2.1.1.8

Multiply $3$ by $2$ .

$3 x + 6 = \frac{3}{2} \cdot 14$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 14$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $14$ .

$3 x + 6 = \frac{3}{2} \cdot (2 (7))$

Step 2.2.1.1.2

Cancel the common factor.

$3 x + 6 = \frac{3}{2} \cdot (2 \cdot 7)$

Step 2.2.1.1.3

Rewrite the expression.

$3 x + 6 = 3 \cdot 7$

Step 2.2.1.2

Multiply $3$ by $7$ .

$3 x + 6 = 21$

Step 3

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

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Step 3.1

Subtract $6$ from both sides of the equation.

$3 x = 21 - 6$

Step 3.2

Subtract $6$ from $21$ .

$3 x = 15$

Step 4

Divide each term in $3 x = 15$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $15$ by $3$ .

$x = 5$