Algebra Examples

$\frac{1}{2} \sqrt{w + 1} = 4$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot \sqrt{w + 1}) = 2 \cdot 4$

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 $2 (\frac{1}{2} \cdot \sqrt{w + 1})$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $\sqrt{w + 1}$ .

$2 \frac{\sqrt{w + 1}}{2} = 2 \cdot 4$

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.

$2 \frac{\sqrt{w + 1}}{2} = 2 \cdot 4$

Step 2.1.1.2.2

Rewrite the expression.

$\sqrt{w + 1} = 2 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $4$ .

$\sqrt{w + 1} = 8$

Step 3

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

${\sqrt{w + 1}}^{2} = 8^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

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

${({(w + 1)}^{\frac{1}{2}})}^{2} = 8^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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Step 4.2.1.1.1

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

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

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

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

Step 4.2.1.1.2.2

Rewrite the expression.

${(w + 1)}^{1} = 8^{2}$

Step 4.2.1.2

Simplify.

$w + 1 = 8^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $8$ to the power of $2$ .

$w + 1 = 64$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$w = 64 - 1$

Step 5.2

Subtract $1$ from $64$ .

$w = 63$