To solve the equation [tex]\(\frac{\sqrt{2k - 3}}{4} = 2\)[/tex], we need to follow these steps:
1. Isolate the square root term:
[tex]\[
\frac{\sqrt{2k - 3}}{4} = 2
\][/tex]
Multiply both sides of the equation by 4 to eliminate the fraction:
[tex]\[
\sqrt{2k - 3} = 4 \times 2
\][/tex]
This simplifies to:
[tex]\[
\sqrt{2k - 3} = 8
\][/tex]
2. Square both sides to eliminate the square root:
[tex]\[
(\sqrt{2k - 3})^2 = 8^2
\][/tex]
This gives:
[tex]\[
2k - 3 = 64
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
Add 3 to both sides of the equation to isolate the term involving [tex]\( k \)[/tex]:
[tex]\[
2k - 3 + 3 = 64 + 3
\][/tex]
This simplifies to:
[tex]\[
2k = 67
\][/tex]
Divide both sides by 2 to solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{67}{2}
\][/tex]
Thus, the solution to the equation [tex]\(\frac{\sqrt{2k - 3}}{4} = 2\)[/tex] is:
[tex]\[
k = \frac{67}{2}
\][/tex]
