Question

what is the solution of $2\sqrt{3x + 4}-9 = 13$? (1 point)\\(x=\square\\)

Explanation:

Step1: Isolate the square root term

Add 9 to both sides of the equation \(2\sqrt{3x + 4}-9 = 13\) to get \(2\sqrt{3x + 4}=13 + 9\).
Simplify the right - hand side: \(2\sqrt{3x + 4}=22\).

Step2: Solve for the square root

Divide both sides of the equation \(2\sqrt{3x + 4}=22\) by 2. We have \(\sqrt{3x + 4}=\frac{22}{2}=11\).

Step3: Eliminate the square root

Square both sides of the equation \(\sqrt{3x + 4}=11\) to get \(3x + 4 = 11^{2}\).
Since \(11^{2}=121\), the equation becomes \(3x+4 = 121\).

Step4: Solve for x

Subtract 4 from both sides: \(3x=121 - 4\).
Simplify the right - hand side: \(3x = 117\).
Divide both sides by 3: \(x=\frac{117}{3}=39\).

Answer:

\(x = 39\)