Pre-Algebra Examples

$\frac{x^{2}}{6} - 4 = 20$

Step 1

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

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Step 1.1

Add $4$ to both sides of the equation.

$\frac{x^{2}}{6} = 20 + 4$

Step 1.2

Add $20$ and $4$ .

$\frac{x^{2}}{6} = 24$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x^{2}}{6} = 6 \cdot 24$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$6 \frac{x^{2}}{6} = 6 \cdot 24$

Step 3.1.1.2

Rewrite the expression.

$x^{2} = 6 \cdot 24$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $6$ by $24$ .

$x^{2} = 144$

Step 4

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

$x = \pm \sqrt{144}$

Step 5

Simplify $\pm \sqrt{144}$ .

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Step 5.1

Rewrite $144$ as $12^{2}$ .

$x = \pm \sqrt{12^{2}}$

Step 5.2

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

$x = \pm 12$

Step 6

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

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Step 6.1

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

$x = 12$

Step 6.2

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

$x = - 12$

Step 6.3

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

$x = 12, - 12$