Pre-Algebra Examples

$\sqrt{6 x - 5} - 7 = 0$

Step 1

Add $7$ to both sides of the equation.

$\sqrt{6 x - 5} = 7$

Step 2

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

${\sqrt{6 x - 5}}^{2} = 7^{2}$

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 $\sqrt{6 x - 5}$ as ${(6 x - 5)}^{\frac{1}{2}}$ .

${({(6 x - 5)}^{\frac{1}{2}})}^{2} = 7^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(6 x - 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(6 x - 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(6 x - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

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.

${(6 x - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(6 x - 5)}^{1} = 7^{2}$

Step 3.2.1.2

Simplify.

$6 x - 5 = 7^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $7$ to the power of $2$ .

$6 x - 5 = 49$

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 $5$ to both sides of the equation.

$6 x = 49 + 5$

Step 4.1.2

Add $49$ and $5$ .

$6 x = 54$

Step 4.2

Divide each term in $6 x = 54$ by $6$ and simplify.

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Step 4.2.1

Divide each term in $6 x = 54$ by $6$ .

$\frac{6 x}{6} = \frac{54}{6}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $6$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{54}{6}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{54}{6}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $54$ by $6$ .

$x = 9$