Algebra Examples

$y = \sqrt{x + 1} - 3$

Step 1

Set $\sqrt{x + 1} - 3$ equal to $0$ .

$\sqrt{x + 1} - 3 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $3$ to both sides of the equation.

$\sqrt{x + 1} = 3$

Step 2.2

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

${\sqrt{x + 1}}^{2} = 3^{2}$

Step 2.3

Simplify each side of the equation.

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Step 2.3.1

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

${({(x + 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

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

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Step 2.3.2.1.1

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

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Step 2.3.2.1.1.1

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

${(x + 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.3.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.3.2.1.1.2.1

Cancel the common factor.

${(x + 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.3.2.1.1.2.2

Rewrite the expression.

${(x + 1)}^{1} = 3^{2}$

Step 2.3.2.1.2

Simplify.

$x + 1 = 3^{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Raise $3$ to the power of $2$ .

$x + 1 = 9$

Step 2.4

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

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Step 2.4.1

Subtract $1$ from both sides of the equation.

$x = 9 - 1$

Step 2.4.2

Subtract $1$ from $9$ .

$x = 8$

Step 3