Solve the Rational Equation for x square root of 6x+1-8=3

$\sqrt{6 x + 1} - 8 = 3$

Move all terms not containing $\sqrt{6 x + 1}$ to the right side of the equation.

Add $8$ to both sides of the equation.

$\sqrt{6 x + 1} = 3 + 8$

Add $3$ and $8$ .

$\sqrt{6 x + 1} = 11$

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

${\sqrt{6 x + 1}}^{2} = 11^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x + 1}$ as ${(6 x + 1)}^{\frac{1}{2}}$ .

${({(6 x + 1)}^{\frac{1}{2}})}^{2} = 11^{2}$

Simplify the left side.

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

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

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

${(6 x + 1)}^{\frac{1}{2} \cdot 2} = 11^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 x + 1)}^{\frac{1}{2} \cdot 2} = 11^{2}$

Rewrite the expression.

${(6 x + 1)}^{1} = 11^{2}$

Simplify.

$6 x + 1 = 11^{2}$

Simplify the right side.

Raise $11$ to the power of $2$ .

$6 x + 1 = 121$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$6 x = 121 - 1$

Subtract $1$ from $121$ .

$6 x = 120$

Divide each term in $6 x = 120$ by $6$ and simplify.

Divide each term in $6 x = 120$ by $6$ .

$\frac{6 x}{6} = \frac{120}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{120}{6}$

Divide $x$ by $1$ .

$x = \frac{120}{6}$

Simplify the right side.

Divide $120$ by $6$ .

$x = 20$