Sure, let's solve the equation step by step:
The given equation is:
[tex]\[
\sqrt{2x - 1} + 3 = 6
\][/tex]
Step 1: Isolate the square root term.
[tex]\[
\sqrt{2x - 1} = 6 - 3
\][/tex]
Step 2: Simplify the right side.
[tex]\[
\sqrt{2x - 1} = 3
\][/tex]
Step 3: Square both sides to eliminate the square root.
[tex]\[
(\sqrt{2x - 1})^2 = 3^2
\][/tex]
Step 4: Simplify both sides.
[tex]\[
2x - 1 = 9
\][/tex]
Step 5: Solve for [tex]\( x \)[/tex].
[tex]\[
2x - 1 = 9 \implies 2x = 9 + 1 \implies 2x = 10 \implies x = \frac{10}{2} \implies x = 5
\][/tex]
So, the solution to the equation [tex]\(\sqrt{2x - 1} + 3 = 6\)[/tex] is:
[tex]\[
x = 5
\][/tex]
