Algebra Examples

$\sqrt{8 x - 1} + 4 = 8$

Step 1

Subtract $8$ from both sides of the equation.

$\sqrt{8 x - 1} + 4 - 8 = 0$

Step 2

Subtract $8$ from $4$ .

$\sqrt{8 x - 1} - 4 = 0$

Step 3

Add $4$ to both sides of the equation.

$\sqrt{8 x - 1} = 4$

Step 4

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

${\sqrt{8 x - 1}}^{2} = 4^{2}$

Step 5

Simplify each side of the equation.

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

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

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Step 5.2.1.1.1

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

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

Step 5.2.1.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.1.2.1

Cancel the common factor.

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

Step 5.2.1.1.2.2

Rewrite the expression.

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

Step 5.2.1.2

Simplify.

$8 x - 1 = 4^{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Raise $4$ to the power of $2$ .

$8 x - 1 = 16$

Step 6

Solve for $x$ .

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Step 6.1

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

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Step 6.1.1

Add $1$ to both sides of the equation.

$8 x = 16 + 1$

Step 6.1.2

Add $16$ and $1$ .

$8 x = 17$

Step 6.2

Divide each term in $8 x = 17$ by $8$ and simplify.

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Step 6.2.1

Divide each term in $8 x = 17$ by $8$ .

$\frac{8 x}{8} = \frac{17}{8}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $8$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{17}{8}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{8}$