Alright, let's solve the inequality step-by-step and write it in its simplest form.
We start with the given inequality:
[tex]\[
-7h - 8 \leq 3h - 7
\][/tex]
Step 1: Eliminate the variable term on one side
To do this, we add [tex]\(7h\)[/tex] to both sides of the inequality:
[tex]\[
-7h - 8 + 7h \leq 3h - 7 + 7h
\][/tex]
Simplifying both sides, we get:
[tex]\[
-8 \leq 10h - 7
\][/tex]
Step 2: Isolate the term involving [tex]\(h\)[/tex]
Next, we add 7 to both sides of the inequality to further isolate [tex]\(h\)[/tex]:
[tex]\[
-8 + 7 \leq 10h - 7 + 7
\][/tex]
This simplifies to:
[tex]\[
-1 \leq 10h
\][/tex]
Step 3: Solve for [tex]\(h\)[/tex]
To solve for [tex]\(h\)[/tex], we divide both sides of the inequality by 10:
[tex]\[
\frac{-1}{10} \leq h
\][/tex]
This simplifies to:
[tex]\[
h \geq -0.1
\][/tex]
So, the solution to the inequality is:
[tex]\[
h \geq -0.1
\][/tex]
Therefore, [tex]\(h\)[/tex] must be greater than or equal to [tex]\(-0.1\)[/tex].
