Question

Given: A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}, B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}

Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A ∩ B.

Answer 1

A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}

= {x : –10 < 5x ≤ 15, x ∈ I}

= {x : –2 < x ≤ 3, x ∈ I}

It can be represented on number line as

B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}

= {x : –9 ≤ 3x < 10, x ∈ R}

= {x : –3 ≤ x < 3.33, x ∈ R}

It can be represeneted on number line as

A ∩ B = {–1, 0, 1, 2, 3}