Sure! Let's solve the inequality to find the values of \( x \) for which \( h(x) > 17 \), where \( h(x) = 3x + 5 \).
1. Start with the inequality:
[tex]\[
3x + 5 > 17
\][/tex]
2. To isolate the term with \( x \), subtract 5 from both sides of the inequality:
[tex]\[
3x + 5 - 5 > 17 - 5
\][/tex]
Simplifying this gives:
[tex]\[
3x > 12
\][/tex]
3. Now, to solve for \( x \), divide both sides of the inequality by 3:
[tex]\[
\frac{3x}{3} > \frac{12}{3}
\][/tex]
Simplifying this gives:
[tex]\[
x > 4
\][/tex]
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( h(x) > 17 \)[/tex] are [tex]\( x > 4 \)[/tex].
