Question

Find the greatest value of x ∈ Z, so that: −1 ≤ 3 + 4x < 23

Answer 1

Given,

−1 ≤ 3 + 4x < 23

Solving L.H.S. of the inequation,

⇒ −1 ≤ 3 + 4x

⇒ −1 − 3 ≤ 4x

⇒ −4 ≤ 4x

⇒ `(-4)/4 ≤ x`

⇒ −1 ≤ x

⇒ x ≥ −1 ....(1)

Solving R.H.S. of the inequation,

⇒ 3 + 4x < 23

⇒ 4x < 23 − 3

⇒ 4x < 20

⇒ x < `20/4`

⇒ x < 5 ....(2)

From (1) and (2) we get,

−1 ≤ x < 5

Since x ∈ Z,

x = {−1, 0, 1, 2, 3, 4}

∴ The greatest value of x is 4.