Certainly! Let's solve the inequality [tex]\(10(2h - 5) \leq 70\)[/tex] step by step.
1. Start with the original inequality:
[tex]\[
10(2h - 5) \leq 70
\][/tex]
2. Distribute the 10 to both terms inside the parentheses:
[tex]\[
10 \cdot 2h - 10 \cdot 5 \leq 70
\][/tex]
This simplifies to:
[tex]\[
20h - 50 \leq 70
\][/tex]
3. Add 50 to both sides of the inequality to isolate the term with [tex]\(h\)[/tex]:
[tex]\[
20h - 50 + 50 \leq 70 + 50
\][/tex]
Simplifying both sides, we get:
[tex]\[
20h \leq 120
\][/tex]
4. Divide both sides by 20 to solve for [tex]\(h\)[/tex]:
[tex]\[
\frac{20h}{20} \leq \frac{120}{20}
\][/tex]
Simplifying the division, we get:
[tex]\[
h \leq 6
\][/tex]
5. Conclusion:
The solution to the inequality [tex]\(10(2h - 5) \leq 70\)[/tex] is:
[tex]\[
h \leq 6
\][/tex]
This means that [tex]\(h\)[/tex] can be any number less than or equal to 6.
