Question

Write the following as intervals: (i) { x : x ∈ R, –4 < x ≤ 6} (ii) { x : x ∈ R, –12 < x < –10} (iii) { x : x ∈ R, 0 ≤ x < 7} (iv) { x : x ∈ R, 3 ≤ x ≤ 4}

Answer 1

(i)

Solving for x,

−4<x≤6 x>−4 x≤6

Further, x is real.

Thus, the set in interval form is ( −4,6 ] .

(ii)

Solving for x,

−12<x<−10 x>−12 x<−10

Further, x is real.

Thus, the set in interval form is ( −12,−10 ) .

(iii)

Solving for x,

0≤x<7 x≥0 x<7

Further, x is real.

Thus, the set in interval form is [ 0,7 ) .

(iv)

Solving for x,

3≤x≤4 x≥3 x≤4

Further, x is real.

Thus, the set in interval form is [ 3,4 ] .