50.6k views
0 votes
Solve: 5-3|2x-5| ≤-1

1 Answer

5 votes

Answer:


\sf \large \: x≥ (7)/(2) or x≤ (3)/(2)

Explanation:

Let's solve your inequality step-by-step.

5−3(|2x−5|)≤−1

−3(|2x−5|)+5≤−1

Step 1: Add -5 to both sides.

−3(|2x−5|)+5+−5≤−1+−5

−3(|2x−5|)≤−6

Step 2: Divide both sides by -3.

−3(|2x−5|)/−3 ≤ −6/−3

|2x−5|≥2

Step 3: Solve Absolute Value.

|2x−5|≥2

We know either2x−5≥2or2x−5≤−2

2x−5≥2(Possibility 1)

2x−5+5≥2+5(Add 5 to both sides)

2x≥7

2x/2 ≥ 7/2

(Divide both sides by 2)

x≥7/2

2x−5≤−2(Possibility 2)

2x−5+5≤−2+5(Add 5 to both sides)

2x≤3

2x/2 ≤ 3/2

(Divide both sides by 2)

x≤ 3/2

User Gieted
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories