Writing and Reading Inequalities Worksheet with Answers

Writing and Reading Inequalities

discia.org 10 questions · 19 marks

Name Date

Either paper 1 mark

\(x\) is no more than \(-1\) and greater than or equal to \(-5\).

Circle the inequality that shows this.

A: \(-5 ≤ x < -1\)

B: \(-5 < x < -1\)

C: \(-5 ≤ x ≤ -1\)

D: \(-5 < x ≤ -1\)

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C: \(-5 ≤ x ≤ -1\)

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Either paper 1 mark

Circle the list of all the integers that satisfy

\(-3 < x ≤ 2\)

A: \(-2,\ -1,\ 0,\ 1,\ 2\)

B: \(-3,\ -2,\ -1,\ 0,\ 1,\ 2\)

C: \(-2,\ -1,\ 0,\ 1\)

D: \(-3,\ -2,\ -1,\ 0,\ 1\)

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\(-2,\ -1,\ 0,\ 1,\ 2\)

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Either paper 2 marks

Here is an inequality.

Write down the inequality shown.

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\(x > 2\)

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Either paper 3 marks

Here is an inequality.

(a)
Write down the inequality shown.

(b)
Write down the largest integer that satisfies this inequality.

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(a) \(x \leq -1\)
(b) \(-1\)

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Either paper 1 mark

\(n\) is an integer.

The largest possible value of \(n\) is \(0\).

Circle the correct inequality.

\(n > 0\) \qquad \(n < 0\) \qquad \(n ≤ 0\) \qquad \(n ≥ 0\)

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\(n ≤ 0\)

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Either paper 3 marks

\(n\) is an integer and \(-2 < n < 3\).

Write down all the possible values of \(n\).

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\(-1, 0, 1, 2\)

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Either paper 3 marks

\(a\) and \(b\) are whole numbers.

\(2 ≤ a ≤ 11\)

\(4 ≤ b < 8\)

(a)
Work out the largest possible value of \(-3a + 5b\).

(b)
\(x\) and \(y\) are both negative numbers.

Show that \(x ÷ y\) could equal \(12\).

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(a) \(29\)
(b) \(x = -36\), \(y = -3\) gives \(-36 ÷ (-3) = 12\)

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Either paper 3 marks

Tick one box for each statement.

	True	May be true	Not true
(i) If a whole number is positive, the number is \(> 1\).	☐	☐	☐
(ii) If a number (not necessarily whole) is \(> -1\), the number is \(≥ 0\).	☐	☐	☐
(iii) If a number (not necessarily whole) is \(> 8\), the number is \(10\).	☐	☐	☐

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Ticks: (i) may be true, (ii) may be true, (iii) may be true

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Either paper 1 mark

\(x\) is greater than or equal to \(-5\) and smaller than \(4\).

Circle the inequality that shows this.

A: \(-5 ≤ x ≤ 4\)

B: \(-5 ≤ x < 4\)

C: \(-5 < x < 4\)

D: \(-5 < x ≤ 4\)

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B: \(-5 ≤ x < 4\)

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Either paper 1 mark

Circle the list of all the integers that satisfy

\(-3 < n ≤ 3\)

A: \(-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3\)

B: \(-2,\ -1,\ 0,\ 1,\ 2\)

C: \(-3,\ -2,\ -1,\ 0,\ 1,\ 2\)

D: \(-2,\ -1,\ 0,\ 1,\ 2,\ 3\)

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\(-2,\ -1,\ 0,\ 1,\ 2,\ 3\)

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discia.org Writing and Reading Inequalities · sheet 1

Answers Writing and Reading Inequalities · sheet 1

C: \(-5 ≤ x ≤ -1\)
\(-2,\ -1,\ 0,\ 1,\ 2\)
\(x > 2\)
(a) \(x \leq -1\)
(b) \(-1\)
\(n ≤ 0\)
\(-1, 0, 1, 2\)
(a) \(29\)
(b) \(x = -36\), \(y = -3\) gives \(-36 ÷ (-3) = 12\)
Ticks: (i) may be true, (ii) may be true, (iii) may be true
B: \(-5 ≤ x < 4\)
\(-2,\ -1,\ 0,\ 1,\ 2,\ 3\)

discia.org Writing and Reading Inequalities · sheet 1