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Absolute inequality
If |x| ≤ p, then x ≤ p and – x ≤ p or x ≥ –p or –p ≤ x ≤ p
If |x|≥ p, then x ≥ p and – x ≥ p or x ≤ –p Therefore, x ≥ p or x ≤ –p
Worked Example 14
Solve |2x – 5| ≥ 13
Solution:
|2x – 5| ≥ 13
–13 ≤ 2x – 5 ≤ 13
Adding 5 on the entire inequality
–13 + 5 ≤ 2x – 5 + 5 ≤ 13 + 5
–8 ≤ 2x ≤ 18
Divide 2 on the entire inequality
–8 ÷ 2 ≤ 2x ÷ 2 ≤ 18 ÷ 2
–4 ≤ x ≤ 9
Worked Example 15
Find the solution set of x – 3 < 7 over a set of square numbers.
Solution:
x–3<7
x < 10
Square numbers less than 10 are: 1, 4 and 9
So, the solution set is {1, 4, 9}
Page 41 of 54
ALGEBRA
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