Solve for x 11+ square root of 1-3x=15

$11 + \sqrt{1 - 3 x} = 15$

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

Subtract $11$ from both sides of the equation.

$\sqrt{1 - 3 x} = 15 - 11$

Subtract $11$ from $15$ .

$\sqrt{1 - 3 x} = 4$

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

${\sqrt{1 - 3 x}}^{2} = 4^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$1 - 3 x = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$1 - 3 x = 16$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$- 3 x = 16 - 1$

Subtract $1$ from $16$ .

$- 3 x = 15$

Divide each term in $- 3 x = 15$ by $- 3$ and simplify.

Divide each term in $- 3 x = 15$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{15}{- 3}$

Divide $x$ by $1$ .

$x = \frac{15}{- 3}$

Simplify the right side.

Divide $15$ by $- 3$ .

$x = - 5$