Solving Inequalities S2 – N7 (S1 – N7 – O)
Recap:
Symbols
> greater than
< less than
≥ greater than or equal to
≤ less than or equal to
= equal
≠ not equal to
Tip to remember
4 > 3
greater = "open mouth" > “point” = less than
Similarly,
3 < 4
less than = “point” < greater = "open mouth"
Example
Solve 7 < 4x – 3 < 13
Step1: Remove number from the expression with x [ 4x – 3]
[+ 3 to all the expression so that the inequalities remain the same]
7 + 3 < 4x – 3 + 3 < 13 + 3
10 < 4x < 16
Step2: Remove the numerical coefficient of x
10 < 4x < 16
4 4 4
2 ½ < x < 4
Multiplication property of Inequalities
x +ve number
if a < b and c > 0, then ac < bc eg: 2 < 3 , x 3 => 6 < 9
If a > b and c > 0, then ac > bc eg: 3 > 2, x 3 => 9 > 6
x –ve number
If a < b and c < 0, then ac > bc eg: 2 < 3 , x -3 => -6 > -9
=> the sign changed from < to >
If a > b and c < 0, then ac < bc eg: 3 > 2 , x -3 => -6 < -9
=> the sign changed from > to <
[[ x –ve : change sign from < to > or > to < ]]
Example
Find the value of x
a. 5x ≥ 15
x ≥ 5 ( Divide both side by +5)
b. -2x > 6
-x < -3 (Divide both side by 2)
-1 x -x > -3 x -1 (We need to solve for x, and not -x)
x < 3 (multiply by -1 => change sign )
