Answer :
To solve the inequality [tex]\(-4s - 9 < -2s - 6\)[/tex], follow these steps:
1. Get all the [tex]\(s\)[/tex] terms on one side of the inequality:
Start by adding [tex]\(4s\)[/tex] to both sides to eliminate the [tex]\(-4s\)[/tex] on the left side:
[tex]\[
-4s + 4s - 9 < -2s + 4s - 6
\][/tex]
This simplifies to:
[tex]\[
-9 < 2s - 6
\][/tex]
2. Isolate the [tex]\(s\)[/tex] term:
Next, add [tex]\(6\)[/tex] to both sides to move the constant term [tex]\(-6\)[/tex] from the right side:
[tex]\[
-9 + 6 < 2s - 6 + 6
\][/tex]
This simplifies to:
[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]
So, the solution in its simplest form is:
[tex]\[
s > -\frac{3}{2}
\][/tex]
This means [tex]\(s\)[/tex] is greater than [tex]\(-1.5\)[/tex].
1. Get all the [tex]\(s\)[/tex] terms on one side of the inequality:
Start by adding [tex]\(4s\)[/tex] to both sides to eliminate the [tex]\(-4s\)[/tex] on the left side:
[tex]\[
-4s + 4s - 9 < -2s + 4s - 6
\][/tex]
This simplifies to:
[tex]\[
-9 < 2s - 6
\][/tex]
2. Isolate the [tex]\(s\)[/tex] term:
Next, add [tex]\(6\)[/tex] to both sides to move the constant term [tex]\(-6\)[/tex] from the right side:
[tex]\[
-9 + 6 < 2s - 6 + 6
\][/tex]
This simplifies to:
[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]
So, the solution in its simplest form is:
[tex]\[
s > -\frac{3}{2}
\][/tex]
This means [tex]\(s\)[/tex] is greater than [tex]\(-1.5\)[/tex].
