Answer :
Sure, let's solve the inequality [tex]\(-4s - 9 < -2s - 6\)[/tex] step-by-step.
1. Move terms involving [tex]\(s\)[/tex] to one side:
We want to bring all the [tex]\(s\)[/tex] terms to one side of the inequality. Add [tex]\(4s\)[/tex] to both sides to help isolate [tex]\(s\)[/tex]:
[tex]\[
-4s + 4s - 9 < -2s + 4s - 6
\][/tex]
Simplifying, we get:
[tex]\[
-9 < 2s - 6
\][/tex]
2. Move constant terms to the other side:
Now, add [tex]\(6\)[/tex] to both sides to move the constant terms:
[tex]\[
-9 + 6 < 2s - 6 + 6
\][/tex]
Simplifying, we obtain:
[tex]\[
-3 < 2s
\][/tex]
3. Solve for [tex]\(s\)[/tex]:
Divide both sides by [tex]\(2\)[/tex] to solve for [tex]\(s\)[/tex]:
[tex]\[
\frac{-3}{2} < s
\][/tex]
Simplifying the inequality, we get:
[tex]\[
s > -\frac{3}{2}
\][/tex]
So, the solution to the inequality is [tex]\(s > -\frac{3}{2}\)[/tex].
1. Move terms involving [tex]\(s\)[/tex] to one side:
We want to bring all the [tex]\(s\)[/tex] terms to one side of the inequality. Add [tex]\(4s\)[/tex] to both sides to help isolate [tex]\(s\)[/tex]:
[tex]\[
-4s + 4s - 9 < -2s + 4s - 6
\][/tex]
Simplifying, we get:
[tex]\[
-9 < 2s - 6
\][/tex]
2. Move constant terms to the other side:
Now, add [tex]\(6\)[/tex] to both sides to move the constant terms:
[tex]\[
-9 + 6 < 2s - 6 + 6
\][/tex]
Simplifying, we obtain:
[tex]\[
-3 < 2s
\][/tex]
3. Solve for [tex]\(s\)[/tex]:
Divide both sides by [tex]\(2\)[/tex] to solve for [tex]\(s\)[/tex]:
[tex]\[
\frac{-3}{2} < s
\][/tex]
Simplifying the inequality, we get:
[tex]\[
s > -\frac{3}{2}
\][/tex]
So, the solution to the inequality is [tex]\(s > -\frac{3}{2}\)[/tex].
