To solve the equation \(\sqrt{3x + 4} = \sqrt{3x} + 4\), you need to proceed with the following detailed steps:
1. Square both sides of the equation:
[tex]\[
\left(\sqrt{3x + 4}\right)^2 = \left(\sqrt{3x} + 4\right)^2
\][/tex]
This results in:
[tex]\[
3x + 4 = 3x + 8\sqrt{3x} + 16
\][/tex]
2. Simplify the equation:
Subtract \(3x\) from both sides:
[tex]\[
4 = 8\sqrt{3x} + 16
\][/tex]
3. Isolate the square root term:
Subtract 16 from both sides:
[tex]\[
-12 = 8\sqrt{3x}
\][/tex]
4. Solve for \(\sqrt{3x}\):
Divide both sides by 8:
[tex]\[
-1.5 = \sqrt{3x}
\][/tex]
5. Square both sides again:
[tex]\[
(-1.5)^2 = (\sqrt{3x})^2
\][/tex]
This results in:
[tex]\[
2.25 = 3x
\][/tex]
6. Solve for \(x\):
Divide by 3:
[tex]\[
x = 0.75
\][/tex]
Based on this detailed procedure, the correct statement is:
Square both sides twice and then solve the resulting linear equation.
