Let's solve the inequality
[tex]\[
\frac{h-7}{10} \leq 60
\][/tex]
step by step.
1. Isolate the term containing [tex]\( h \)[/tex]:
We begin by isolating the term containing [tex]\( h \)[/tex] by eliminating the fraction. To do this, we multiply both sides of the inequality by 10, which is the denominator.
[tex]\[
10 \cdot \frac{h-7}{10} \leq 10 \cdot 60
\][/tex]
2. Simplify the inequality:
The multiplication eliminates the fraction on the left-hand side.
[tex]\[
h - 7 \leq 600
\][/tex]
3. Solve for [tex]\( h \)[/tex]:
Next, we isolate [tex]\( h \)[/tex] by adding 7 to both sides of the inequality to get [tex]\( h \)[/tex] alone on one side.
[tex]\[
h - 7 + 7 \leq 600 + 7
\][/tex]
Simplifying this gives:
[tex]\[
h \leq 607
\][/tex]
4. Express the solution:
We interpret the result as [tex]\( h \)[/tex] can be any real number less than or equal to 607. Formally, this can be written in interval notation or using inequality notation. Because there is no lower bound strictly defined, [tex]\( h \)[/tex] can be any real number from [tex]\(-\infty\)[/tex] up to and including 607.
5. Final Answer:
The solution to the inequality [tex]\(\frac{h-7}{10} \leq 60\)[/tex] is:
[tex]\[
h \leq 607
\][/tex]
Or in interval notation:
[tex]\[
(-\infty, 607]
\][/tex]
