Pre-Algebra Examples

${(\sqrt{3 x - 2})}^{2} = 100$

Step 1

Rewrite ${\sqrt{3 x - 2}}^{2}$ as $3 x - 2$ .

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Step 1.1

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

${({(3 x - 2)}^{\frac{1}{2}})}^{2} = 100$

Step 1.2

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

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 100$

Step 1.3

Combine $\frac{1}{2}$ and $2$ .

${(3 x - 2)}^{\frac{2}{2}} = 100$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

${(3 x - 2)}^{\frac{2}{2}} = 100$

Step 1.4.2

Rewrite the expression.

${(3 x - 2)}^{1} = 100$

Step 1.5

Simplify.

$3 x - 2 = 100$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

$3 x = 100 + 2$

Step 2.2

Add $100$ and $2$ .

$3 x = 102$

Step 3

Divide each term in $3 x = 102$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = 102$ by $3$ .

$\frac{3 x}{3} = \frac{102}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{102}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{102}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $102$ by $3$ .

$x = 34$