What is the solution to the inequality \( 8 - \frac{4}{5}f > -14 - 2f \)?

8-4/5f>-14-2f
(subtract 8 on both sides)
-4/5f>-22-2f
(add 2f on both sides)
6/5f>-22
(divide 6/5 on both sides)
f>-55/3(-18.33)

Answered by lekhagummalla | 2024-06-10

-14-2f\ \ \ \ \ |\cdot5\\\\40-4f>-70-10f\\\\-4f+10f>-70-40\\\\6f>-110\ \ \ \ \ |:6\\\\f>-\frac{110}{6}\\\\f>-\frac{55}{3}\\\\f\in(-\frac{55}{3},\infty)"> 8 − 5 4 ​ f > − 14 − 2 f ∣ ⋅ 5 40 − 4 f > − 70 − 10 f − 4 f + 10 f > − 70 − 40 6 f > − 110 ∣ : 6 f > − 6 110 ​ f > − 3 55 ​ f ∈ ( − 3 55 ​ , ∞ )

Answered by luana | 2024-06-10

To solve the inequality -14 - 2f"> 8 − 5 4 ​ f > − 14 − 2 f , we isolate f , rearranging and simplifying to find that -\frac{55}{3}"> f > − 3 55 ​ . This means that f must be greater than approximately -18.33. Therefore, the solution set consists of all values of f greater than -18.33.
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Answered by Anonymous | 2024-10-27