Workout
Question 1:
(a) 1 < x < 4
(b) -1 < x < 2
(c) -7 ≤ x ≤ -3
(d) -4 ≤ x ≤ 5
(e) x < 0 or x > 9
(f) x < -6 or x > 5
(g) x ≤ -10 or x ≥ -1
(h) x ≤ -7 or x ≥ 7
(i) -8 < x < -2
(j) x ≤ -7 or x ≥ 4
(k) -1 ≤ x ≤ 5
(l) x < 12 or x > 11
Question 2
(a) x < -3 or x > -2
(b) -5 < x < -2
(c) -1 ≤ x ≤ 5
(d) x <-6 or x >4
(e) x ≤ 2 or x ≥ 4
(f) -4 < x < 1
(g) x < -7 or x > 8
(h) – 6 < x < -3
(i) 2 ≤ x ≤ 11
(j) – 4 < x < 8
(k) x ≤ -8 or x ≥ 8
(l) x < 6 or x > 8
Question 3:
(a) -3 < x < 5
(b) x < -4 or x > -1
(c) -6 < x < 6
(d) x < -11 or x > 11
(e) -4 ≤ x ≤ 3
(f) 4 < x < 10
(g) -18 < x < 2
(h) x ≤ -4 or x ≥ 6
Question 4:
(a) x < 3 or x > 5
(b) -2 ≤ x ≤ 5
(c) x ≤ -5 or x ≥ -1
(d) 2 < x < 16
(e) x < -4 or x > 11
(f) x < -1 or x > 0
Question 5:
(a) 0.5 < x < 4
(b) x < -4 or x > -0.2
(c) -3.5 ≤ x ≤ 8
(d) -1 ≤ x ≤ 0.66666…
(e) x < 0.75 or x > 4.5
(f) x ≤ -0.6666… or x ≥ 1.666…
Question 6:
(a) x < -1 or x > -0.4
(b) – 3 < x < 0.3333…
(c) x < 0.5 or x > 4
(d) x ≤ -0.25 or x ≥ 1
(e) 1 < x < 1.1666666..
(f) -2 ≤ x ≤ 1.5
(g) x < 0.75 or x > 2
(h) x ≤ 0.75 or x ≥ 6
(i) -1.666… < x < 1.4
Apply
Question 1:
Mistake 1 – Tia really should sketch a graph (or use a table/number line depending on your own preference)
Mistake 2 – The answer should be x < -3 or x > 11. A graph would help Tia with that 🙂
Question 2:
(a) x = -3 + √6 or x = -3 – √6
(b) -3 – √6 < x < -3 + √6
Question 3: x² + 7x + 10 < 0
Question 4: x² – 3x – 18 > 0
Question 5: 1.5 < x < 10
Question 6: (2x + 1)(2x – 3) > 0
4x² – 4x – 3 > 0
Question 7: 50 < x < 110
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