Question

Solve the inequation:

3z – 5 ≤ z + 3 < 5z – 9; z ∈ R.

Graph the solution set on the number line.

Answer 1

3z – 5 ≤ z + 3 < 5z – 9

3z – 5 ≤ z + 3 and z + 3 < 5z – 9

2z ≤ 8 and 12 < 4z

Z ≤ 4 and 3 < z

Since, z ∈ R

∴ Solution set = {3 < z ≤ 4, x ∈ R}

It can be represented on a number line as: