Let's solve the equation [tex]\(\sqrt{3m + 1} - 2 = 0\)[/tex] step-by-step.
1. Start with the original equation:
[tex]\[
\sqrt{3m + 1} - 2 = 0
\][/tex]
2. Isolate the square root term by adding 2 to both sides of the equation:
[tex]\[
\sqrt{3m + 1} = 2
\][/tex]
3. To eliminate the square root, square both sides of the equation:
[tex]\[
(\sqrt{3m + 1})^2 = 2^2
\][/tex]
Simplifying the squares gives:
[tex]\[
3m + 1 = 4
\][/tex]
4. Solve for [tex]\(m\)[/tex] by first subtracting 1 from both sides:
[tex]\[
3m = 3
\][/tex]
5. Finally, divide both sides of the equation by 3:
[tex]\[
m = 1
\][/tex]
So, the value of [tex]\(m\)[/tex] is [tex]\(1\)[/tex].
Therefore, the correct answer is:
c. 1
