Pre-Algebra Examples

$24 = x \cdot \frac{2}{3} \cdot x$

Step 1

Rewrite the equation as $x \cdot \frac{2}{3} \cdot x = 24$ .

$x \cdot \frac{2}{3} \cdot x = 24$

Step 2

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

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Step 2.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.1

Move $x$ .

$x \cdot x \cdot \frac{2}{3} = 24$

Step 2.1.2

Multiply $x$ by $x$ .

$x^{2} \cdot \frac{2}{3} = 24$

Step 2.2

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

$\frac{x^{2} \cdot 2}{3} = 24$

Step 2.3

Move $2$ to the left of $x^{2}$ .

$\frac{2 x^{2}}{3} = 24$

Step 3

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

$\frac{3}{2} \cdot \frac{2 x^{2}}{3} = \frac{3}{2} \cdot 24$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 x^{2}}{3}$ .

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Step 4.1.1.1

Combine.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 24$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 24$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 24$

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 24$

Step 4.1.1.3.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{3}{2} \cdot 24$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} \cdot 24$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $24$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

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

Step 4.2.1.2

Multiply $3$ by $12$ .

$x^{2} = 36$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{36}$

Step 6

Simplify $\pm \sqrt{36}$ .

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Step 6.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Step 6.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 6$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 7.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

Step 7.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6$

Step 7.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 6, - 6$