Pre-Algebra Examples

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

Step 1

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

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

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

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Step 2.1.1.1

Combine.

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

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

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

Step 2.1.1.2.2

Rewrite the expression.

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

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Cancel the common factor.

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

Step 2.1.1.3.2

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

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $24$ .

$x^{2} = \frac{2}{3} \cdot (3 (8))$

Step 2.2.1.1.2

Cancel the common factor.

$x^{2} = \frac{2}{3} \cdot (3 \cdot 8)$

Step 2.2.1.1.3

Rewrite the expression.

$x^{2} = 2 \cdot 8$

Step 2.2.1.2

Multiply $2$ by $8$ .

$x^{2} = 16$

Step 3

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

$x = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

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Step 4.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

Step 4.2

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

$x = \pm 4$

Step 5

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

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Step 5.1

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

$x = 4$

Step 5.2

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

$x = - 4$

Step 5.3

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

$x = 4, - 4$