Inequation and graph the solution on the number line.

Given that x ∈ R, solve the following inequation and graph the solution on the number line: – 1 ≤ 3 + 4x < 23. (2006)

Solution:

We have
– 1 ≤ 3 + 4x < 23 ⇒ – 1 – 3 ≤ 4x < 23 – 3 ⇒ – 4 ≤ 4x < 20 ⇒ – 1 ≤ x < 5, x ∈ R
Solution Set = { – 1 ≤ x < 5; x ∈ R}

Solve the following inequation and graph the solution on the number line. (2007)
x∈R

Solution:

Given  x∈R

Multiplying by 3, L.C.M. of fractions, we get