Answer :
To solve the compound inequality [tex]\(14 > 17f - 3 \geq -20\)[/tex], we need to break it down into two separate inequalities and solve each one:
1. Solve the inequality [tex]\(14 > 17f - 3\)[/tex]:
- First, add 3 to both sides to isolate the term with [tex]\(f\)[/tex]:
[tex]\[
14 + 3 > 17f
\][/tex]
[tex]\[
17 > 17f
\][/tex]
- Divide both sides by 17 to solve for [tex]\(f\)[/tex]:
[tex]\[
\frac{17}{17} > f
\][/tex]
[tex]\[
1 > f
\][/tex]
So, the solution to this inequality is [tex]\(f < 1\)[/tex].
2. Solve the inequality [tex]\(17f - 3 \geq -20\)[/tex]:
- Add 3 to both sides to isolate the term with [tex]\(f\)[/tex]:
[tex]\[
17f - 3 + 3 \geq -20 + 3
\][/tex]
[tex]\[
17f \geq -17
\][/tex]
- Divide both sides by 17 to solve for [tex]\(f\)[/tex]:
[tex]\[
f \geq \frac{-17}{17}
\][/tex]
[tex]\[
f \geq -1
\][/tex]
Now, combine the solutions of both inequalities. The compound inequality is:
[tex]\[
-1 \leq f < 1
\][/tex]
This means [tex]\(f\)[/tex] can be any number between -1 and 1, including -1 but not 1.
1. Solve the inequality [tex]\(14 > 17f - 3\)[/tex]:
- First, add 3 to both sides to isolate the term with [tex]\(f\)[/tex]:
[tex]\[
14 + 3 > 17f
\][/tex]
[tex]\[
17 > 17f
\][/tex]
- Divide both sides by 17 to solve for [tex]\(f\)[/tex]:
[tex]\[
\frac{17}{17} > f
\][/tex]
[tex]\[
1 > f
\][/tex]
So, the solution to this inequality is [tex]\(f < 1\)[/tex].
2. Solve the inequality [tex]\(17f - 3 \geq -20\)[/tex]:
- Add 3 to both sides to isolate the term with [tex]\(f\)[/tex]:
[tex]\[
17f - 3 + 3 \geq -20 + 3
\][/tex]
[tex]\[
17f \geq -17
\][/tex]
- Divide both sides by 17 to solve for [tex]\(f\)[/tex]:
[tex]\[
f \geq \frac{-17}{17}
\][/tex]
[tex]\[
f \geq -1
\][/tex]
Now, combine the solutions of both inequalities. The compound inequality is:
[tex]\[
-1 \leq f < 1
\][/tex]
This means [tex]\(f\)[/tex] can be any number between -1 and 1, including -1 but not 1.
