Algebra Examples

$10 = 3 \sqrt{5 x - 1} - 2$

Step 1

Rewrite the equation as $3 \sqrt{5 x - 1} - 2 = 10$ .

$3 \sqrt{5 x - 1} - 2 = 10$

Step 2

Move all terms not containing $3 \sqrt{5 x - 1}$ to the right side of the equation.

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Step 2.1

Add $2$ to both sides of the equation.

$3 \sqrt{5 x - 1} = 10 + 2$

Step 2.2

Add $10$ and $2$ .

$3 \sqrt{5 x - 1} = 12$

Step 3

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

${(3 \sqrt{5 x - 1})}^{2} = 12^{2}$

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 $\sqrt{5 x - 1}$ as ${(5 x - 1)}^{\frac{1}{2}}$ .

${(3 {(5 x - 1)}^{\frac{1}{2}})}^{2} = 12^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(3 {(5 x - 1)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Apply the product rule to $3 {(5 x - 1)}^{\frac{1}{2}}$ .

$3^{2} {({(5 x - 1)}^{\frac{1}{2}})}^{2} = 12^{2}$

Step 4.2.1.2

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

$9 {({(5 x - 1)}^{\frac{1}{2}})}^{2} = 12^{2}$

Step 4.2.1.3

Multiply the exponents in ${({(5 x - 1)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.3.1

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

$9 {(5 x - 1)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Step 4.2.1.3.2

Cancel the common factor of $2$ .

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Step 4.2.1.3.2.1

Cancel the common factor.

$9 {(5 x - 1)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Step 4.2.1.3.2.2

Rewrite the expression.

$9 {(5 x - 1)}^{1} = 12^{2}$

Step 4.2.1.4

Simplify.

$9 (5 x - 1) = 12^{2}$

Step 4.2.1.5

Apply the distributive property.

$9 (5 x) + 9 \cdot - 1 = 12^{2}$

Step 4.2.1.6

Multiply.

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Step 4.2.1.6.1

Multiply $5$ by $9$ .

$45 x + 9 \cdot - 1 = 12^{2}$

Step 4.2.1.6.2

Multiply $9$ by $- 1$ .

$45 x - 9 = 12^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $12$ to the power of $2$ .

$45 x - 9 = 144$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Add $9$ to both sides of the equation.

$45 x = 144 + 9$

Step 5.1.2

Add $144$ and $9$ .

$45 x = 153$

Step 5.2

Divide each term in $45 x = 153$ by $45$ and simplify.

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Step 5.2.1

Divide each term in $45 x = 153$ by $45$ .

$\frac{45 x}{45} = \frac{153}{45}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $45$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{45 x}{45} = \frac{153}{45}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{153}{45}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $153$ and $45$ .

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Step 5.2.3.1.1

Factor $9$ out of $153$ .

$x = \frac{9 (17)}{45}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $9$ out of $45$ .

$x = \frac{9 \cdot 17}{9 \cdot 5}$

Step 5.2.3.1.2.2

Cancel the common factor.

$x = \frac{9 \cdot 17}{9 \cdot 5}$

Step 5.2.3.1.2.3

Rewrite the expression.

$x = \frac{17}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{5}$

Decimal Form:

$x = 3.4$

Mixed Number Form:

$x = 3 \frac{2}{5}$