To find the value of [tex]\( x \)[/tex] that satisfies [tex]\( s(x) = 17 \)[/tex] for the function [tex]\( s(x) = \sqrt{5x + 6} + 8 \)[/tex], follow these steps:
1. Start with the given function and set it equal to 17:
[tex]\[
\sqrt{5x + 6} + 8 = 17
\][/tex]
2. Isolate the square root term:
[tex]\[
\sqrt{5x + 6} = 17 - 8
\][/tex]
3. Simplify the right-hand side:
[tex]\[
\sqrt{5x + 6} = 9
\][/tex]
4. Square both sides to eliminate the square root:
[tex]\[
(\sqrt{5x + 6})^2 = 9^2
\][/tex]
5. Simplify both sides:
[tex]\[
5x + 6 = 81
\][/tex]
6. Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
5x = 81 - 6
\][/tex]
[tex]\[
5x = 75
\][/tex]
[tex]\[
x = \frac{75}{5}
\][/tex]
[tex]\[
x = 15
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies [tex]\( s(x) = 17 \)[/tex] for the given function is:
[tex]\[
x = 15
\][/tex]
