Question

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

Answer 1

6/5 < x < 10/3 is the desired solution.

Explanation:

Here, the given compound inequality is :

x + 1 < -2 x + 11 < 3 x + 5

Now, 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 + 10

or, x + 2x < 10

or, 3 x < 10

or, x < 10/3

Similarly, considering the last two terms of the given inequality, we get:

-2 x + 11 < 3 x + 5

Subtracting 11 from both sides, we get:

-2 x + 11 - 11 < 3 x + 5 - 11

or, - 2 x < 3 x-6

or, 6 < 5 x

or, x > 6/5

Hence, combining two solutions, we get: 6/5 < x < 10/3

So, the desired value of x should be more than (6/5) but less than (10/3)