Precalculus Examples

$5 = \sqrt{4 x - 3}$

Step 1

Rewrite the equation as $\sqrt{4 x - 3} = 5$ .

$\sqrt{4 x - 3} = 5$

Step 2

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

${\sqrt{4 x - 3}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x - 3}$ as ${(4 x - 3)}^{\frac{1}{2}}$ .

${({(4 x - 3)}^{\frac{1}{2}})}^{2} = 5^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(4 x - 3)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(4 x - 3)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(4 x - 3)}^{1} = 5^{2}$

Step 3.2.1.2

Simplify.

$4 x - 3 = 5^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $5$ to the power of $2$ .

$4 x - 3 = 25$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $3$ to both sides of the equation.

$4 x = 25 + 3$

Step 4.1.2

Add $25$ and $3$ .

$4 x = 28$

Step 4.2

Divide each term in $4 x = 28$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 x = 28$ by $4$ .

$\frac{4 x}{4} = \frac{28}{4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{28}{4}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{4}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $28$ by $4$ .

$x = 7$