To solve the equation [tex]\( 11 + \sqrt{1 - 3x} = 15 \)[/tex] for [tex]\( x \)[/tex], we can follow these steps:
1. Isolate the square root term:
- We start by subtracting 11 from both sides of the equation:
[tex]\[
11 + \sqrt{1 - 3x} - 11 = 15 - 11
\][/tex]
- Simplifying both sides, we get:
[tex]\[
\sqrt{1 - 3x} = 4
\][/tex]
2. Remove the square root by squaring both sides:
- To eliminate the square root, we square both sides of the equation:
[tex]\[
(\sqrt{1 - 3x})^2 = 4^2
\][/tex]
- Simplifying, we obtain:
[tex]\[
1 - 3x = 16
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- First, isolate the term containing [tex]\( x \)[/tex] by subtracting 1 from both sides:
[tex]\[
1 - 3x - 1 = 16 - 1
\][/tex]
- This simplifies to:
[tex]\[
-3x = 15
\][/tex]
- Finally, divide both sides by -3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{15}{-3}
\][/tex]
- Simplifying this, we get:
[tex]\[
x = -5
\][/tex]
Therefore, the solution to the equation [tex]\( 11 + \sqrt{1 - 3x} = 15 \)[/tex] is [tex]\( x = -5 \)[/tex].
The correct answer is:
D. [tex]\( x = -5 \)[/tex]
