Algebra 9

2 marks · Normal

Give a counter-example to show that the statement below is false:

The difference between two numbers is always less than their sum.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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Example: 1 and -1. Their difference is 2, and their sum is 0.

Must show: Any valid example where difference > sum

Also accept: Numbers: 4 and -4 (difference 8, sum 0); Numbers: 2 and -2 (difference 4, sum 0)

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Marking points

B1 · 1 mark · Finds a valid pair of numbers (including a negative) as counter-example.

B2 · 1 mark · Clearly shows, using those numbers, that their difference is greater than their sum.

Worked solution

Take 1 and -1:

Difference: 1 - (-1) = 2

Sum: 1 + (-1) = 0

Here, the difference (2) is greater than the sum (0), so the statement is false.