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Numerical Inequalities · Question 1 of 79

Question 1

EasyOriginal question

a<ba < b. Which of these is always true?

Options for question 1

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Multiplying both sides by a negative number reverses the inequality: a<ba < b gives −3a>−3b-3a > -3b.

  2. The others fail: −3<1-3 < 1 but 9>19 > 1; a=−1a = -1, b=1b = 1 give reciprocals −1-1 and 1, still in the same order; and subtracting 5 keeps <<.

Worth noting

a2<b2a^{2} < b^{2} holds for positive numbers only: −3<1-3 < 1, yet 9>19 > 1.

Concept
Multiplying by a negative number
Typical time
60 s
Your time
—
The rule this testsThe laws of inequality
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Ten questions from Numerical Inequalities, at your own pace.

Practise this chapter →

Ten questions from Numerical Inequalities, at your own pace.