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What is the solution to the equation below?

[tex]\[ 2 + \sqrt{3x + 4} = 6 \][/tex]

A. [tex]\( x = -\frac{20}{3} \)[/tex]

B. [tex]\( x = -\frac{2}{3} \)[/tex]

C. [tex]\( x = 16 \)[/tex]

D. [tex]\( x = 4 \)[/tex]

Sagot :

GinnyAnsweridn
Let's solve the equation step by step:

Given equation:
[tex]\[ 2 + \sqrt{3x + 4} = 6 \][/tex]

1. Isolate the square root term:
[tex]\[ \sqrt{3x + 4} = 6 - 2 \][/tex]
[tex]\[ \sqrt{3x + 4} = 4 \][/tex]

2. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{3x + 4})^2 = 4^2 \][/tex]
[tex]\[ 3x + 4 = 16 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
[tex]\[ 3x + 4 = 16 \][/tex]
[tex]\[ 3x = 16 - 4 \][/tex]
[tex]\[ 3x = 12 \][/tex]
[tex]\[ x = \frac{12}{3} \][/tex]
[tex]\[ x = 4 \][/tex]

Therefore, the solution to the equation [tex]\( 2 + \sqrt{3x + 4} = 6 \)[/tex] is:
[tex]\[ D. \, x = 4 \][/tex]
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