1. ©G Dear2008 – Not to be sold/Free to use
Mathematic
(Preliminary)
Equations
Absolute Equations
Stage 6 - Year 12
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©G Dear2008 – Not to be sold/Free to use

2. Equations Absolute Equations Properties If a > 0 then |a| = a

3. Equations Absolute Equations Examples 1 1. |x| = 7 2. |x| ≤ 3
x = -7 and + 7 -7 7 -3 3

4. Equations Absolute Equations Example 2 |x + 3| = 7
Therefore x + 3 = -7
and x + 3 = +7
x = -4
x = 4 -4 4

5. Equations Absolute Equations Example 3 |2x - 3| ≤ 5
Therefore 2x - 3 ≥ -5
and 2x - 3 ≤ 5
i.e. between -5 and +5
2x ≥ -2
2x ≤ 8
x ≥ -1
x ≤ 4 -1 4