Algebra Examples

$\sqrt{\frac{2 x - 4}{8}} = 2$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{2 x - 4}{8}}}^{2} = 2^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{2 x - 4}{8}}$ as ${(\frac{2 x - 4}{8})}^{\frac{1}{2}}$ .

${({(\frac{2 x - 4}{8})}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(\frac{2 x - 4}{8})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(\frac{2 x - 4}{8})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{2 x - 4}{8})}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(\frac{2 x - 4}{8})}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(\frac{2 x - 4}{8})}^{1} = 2^{2}$

Step 2.2.1.2

Cancel the common factor of $2 x - 4$ and $8$ .

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Step 2.2.1.2.1

Factor $2$ out of $2 x$ .

${(\frac{2 (x) - 4}{8})}^{1} = 2^{2}$

Step 2.2.1.2.2

Factor $2$ out of $- 4$ .

${(\frac{2 x + 2 \cdot - 2}{8})}^{1} = 2^{2}$

Step 2.2.1.2.3

Factor $2$ out of $2 x + 2 \cdot - 2$ .

${(\frac{2 (x - 2)}{8})}^{1} = 2^{2}$

Step 2.2.1.2.4

Cancel the common factors.

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Step 2.2.1.2.4.1

Factor $2$ out of $8$ .

${(\frac{2 (x - 2)}{2 (4)})}^{1} = 2^{2}$

Step 2.2.1.2.4.2

Cancel the common factor.

${(\frac{2 (x - 2)}{2 \cdot 4})}^{1} = 2^{2}$

Step 2.2.1.2.4.3

Rewrite the expression.

${(\frac{x - 2}{4})}^{1} = 2^{2}$

Step 2.2.1.3

Simplify.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $2$ to the power of $2$ .

$\frac{x - 2}{4} = 4$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides of the equation by $4$ .

$4 \frac{x - 2}{4} = 4 \cdot 4$

Step 3.2

Simplify both sides of the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Cancel the common factor.

$4 \frac{x - 2}{4} = 4 \cdot 4$

Step 3.2.1.1.2

Rewrite the expression.

$x - 2 = 4 \cdot 4$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $4$ by $4$ .

$x - 2 = 16$

Step 3.3

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

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Step 3.3.1

Add $2$ to both sides of the equation.

$x = 16 + 2$

Step 3.3.2

Add $16$ and $2$ .

$x = 18$