MATH SOLVE

4 months ago

Q:
# What is the solution set of the compound inequality x+1<-2x+11<3x+5

Accepted Solution

A:

Answer: 6/5 < x < 10/3 is the desired solution.Step-by-step explanation:Here, the given compound inequality is :x + 1 < -2 x + 11 < 3 x + 5Now, consider the first two term of the inequality, we get:x + 1 < -2 x + 11 Subtracting 1 from both sides, we get:x + 1 - 1 < -2 x + 11 - 1 or, x < -2x + 10or, x + 2x < 10or, 3 x < 10 or, x < 10/3Similarly, considering the last two terms of the given inequality, we get: -2 x + 11 < 3 x + 5Subtracting 11 from both sides, we get: -2 x + 11 - 11 < 3 x + 5 - 11or, - 2 x < 3 x-6 or, 6 < 5 xor, x > 6/5Hence, combining two solutions, we get: 6/5 < x < 10/3So, the desired value of x should be more than (6/5) but less than (10/3)