Algebra Examples

$\frac{2}{3} x = 12$

Step 1

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

$\frac{3}{2} (\frac{2}{3} x) = \frac{3}{2} \cdot 12$

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 $\frac{3}{2} (\frac{2}{3} x)$ .

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Step 2.1.1.1

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

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 12$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 12$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 12$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot 12$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 12$

Step 2.1.1.3.3

Rewrite the expression.

$x = \frac{3}{2} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 12$ .

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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 $12$ .

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

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 6$

Step 2.2.1.2

Multiply $3$ by $6$ .

$x = 18$