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Solve for [tex]f[/tex].

[tex]14 \ > \ 17f - 3 \geq -20[/tex]

Write your answer as a compound inequality.

[tex]\square[/tex]

Answer :

To solve the compound inequality [tex]\(14 > 17f - 3 \geq -20\)[/tex], we will break it into two separate inequalities and solve for [tex]\(f\)[/tex] in each of them.

1. Solve the left part of 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]

- Next, divide both sides by 17 to solve for [tex]\(f\)[/tex]:

[tex]\(f < \frac{17}{17}\)[/tex]

[tex]\(f < 1\)[/tex]

2. Solve the right part of the inequality:

[tex]\(17f - 3 \geq -20\)[/tex]

- First, add 3 to both sides to isolate the term with [tex]\(f\)[/tex]:

[tex]\(17f \geq -20 + 3\)[/tex]

[tex]\(17f \geq -17\)[/tex]

- Next, divide both sides by 17 to solve for [tex]\(f\)[/tex]:

[tex]\(f \geq \frac{-17}{17}\)[/tex]

[tex]\(f \geq -1\)[/tex]

3. Combine the results:

The solution for the compound inequality is [tex]\(-1 \leq f < 1\)[/tex].

So, [tex]\(f\)[/tex] is in the range [tex]\([-1, 1)\)[/tex].

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