Past Papers Worksheet
Linear Inequality
1. Solve the following inequalities:
(a) 3n – 11 > 5n – 18
(b) 3n – 5 >17 + 8n
(e) n + 7 < 5n - 8
(f) 5t + 23 < 17 – 2t
𝑥
(i) 5(𝓍 – 4) < 3(12 – 𝓍)
(m)
2. (a)
(b)
2𝑥+1
3
≤
(j) 2 − 13 > 12 + 3𝑥
5𝑥−8
4
(n) 2𝑥 + 5 <
𝑥−1
4
IGCSE Mathematics 0580
(c) 7 – 8𝓍 ≥ 19 + 2𝓍
(g) 3𝓍 – 1 ≤ 11𝓍 + 2
(k)
(o)
2𝑥−3
𝑥
− 3
5
𝑥
+5>2
3
≤2
(d) 6n + 3 > 8n
(h) 7𝓍 – 5 > 3(2 – 5𝓍)
(l) 6(2 – 3𝓍) − 4(1 – 2𝓍) ≤ 0
𝑥
(p) 2 +
𝑥−2
3
<5
List the positive integers that satisfy the inequality 𝓍 + 13 ≥ 3𝓍 + 7
Find the positive integers that satisfy the inequality t + 2 > 3t – 6
21+𝑥
5
(c)
Solve the inequality for positive integer values of 𝓍
(d)
(e)
(f)
(g)
(h)
(i)
Find the integer values of n that satisfy the inequalities 15 ≤ 4n < 28
Find the integers which satisfy the inequality -5 < 2n – 1 ≤ 5
Find the integer values of n that satisfy this inequality -7 < 4n ≤ 8
Find the integer values of n that satisfy the inequality 18 – 2n < 6n ≤ 30 + n
Find the integer values for 𝓍 which satisfy the inequality –3 < 2𝓍 –1 ≤ 6
List all the prime numbers which satisfy this inequality 16 < 2𝓍 – 5 < 48
2
>𝑥+1
1
Q-3.
Given that –4 3 ≤ 2k ≤ 17 3 write down
(a) the smallest integer value of k
(b) the largest prime value of k
(c) the largest rational value of k
Q-4.
Given that x is an integer, find the largest possible value of x which satisfies the following inequality:
2
6 – x ≥ 3 (x – 8)
Q-5.
Solve the inequality 5(2x – 3) ≥ 14 – x and state the smallest possible value of x if x is an integer.
Q-6.
Solve the inequality 2x – 1 ≥ 11 + 5x and write down the largest integer value of x.
Q-7.
Given that –2 ≤ x ≤ 3.5 and 2 ≤ y ≤ 5
(a)
list the integer values of x
(b)
write down the largest rational value of x
2𝑥
(c)
calculate the smallest possible value of (i) (x – y)2
(ii) x2 – y2
(iii) 𝑦
Q-8
Given that −5 ≤ 4x – 1 ≤ 2x + 7 and −6 ≤ 3y ≤ 15, find
1
2
(a)
(b)
(c)
(d)
Q-9
1
4
the greatest possible value of x + y
the smallest possible value of x – y
the greatest possible value of x2 – y2
the smallest possible value of x2 + y2
Given that −5 ≤ x ≤ − 1 and 1 ≤ y ≤ 6, find
(a)
(b)
(c)
the greatest possible value of 2x – y
the greatest possible value of y – 4x
𝑦
the least possible value of 𝑥
(d)
the least possible value of
𝑥
𝑦
Q-10 A woman buys x oranges at 50 cents each and (2x + 1) pineapples at $1.20 each. If she wishes to spend not more
than $25 on these produce,
(a)
(b)
Q-11
form an inequality in x, and
find the largest number of x
A music shop is having a sale and each compact disc is priced at $12.49. A man has $97 in his pocket. What is the
maximum number of compact discs that he can buy?
ANSWERS:
1.
(a) n < 3.5
(g) 𝓍 ≥ - 3/8
(m) 𝓍 ≥ 4
(b) n < -4.4
(h) 𝓍 > 0.5
(n) 𝓍 < -3
(c) 𝓍 ≤ -1.2
(i) 𝓍 < 7
(o) 𝓍 > -9
2.
(a) 1, 2, 3
(g) 3, 4, 5, 6
(b) 1, 2, 3
(h) 0, 1, 2, 3
(c) 1, 2, 3
(d) 4, 5, 6
(i) 11, 13, 17, 19, 23
3.
(a) -2
(b) 7
4.
6
7.
(a) -2, -1, 0, 1, 2, 3
(b)
8.
(a) 9
(b) -6
(c) 16
(d) 0
9.
(a) -3
(b) 26
(c)
(d)
10.
(a)
11.
7
(e) n > 3.75
(k) 𝓍 ≤ 39
(f) t < -6/7
(l) 𝓍 ≥ 0.8
(e) –1, 0, 1, 2, 3
(f) −1, 0, 1, 2
𝟐
(c) 𝟖 𝟑
5.
2.9x ≤ 23.8
(d) n < 1.5
(j) 𝓍 < -10
(p) 𝓍 < 6.8
(b)
3
8
6.
4
3.5
-6
(c)i) 0
-5
ii) -25
(iii)
-2