Absolute Value

جامعة بابل / كلية التربية للعلوم الصرفة / قسم الرياضيات 11 ( رياضيات ) 20
1
Intervals
Types of intervals
Inequalities
جامعة بابل / كلية التربية للعلوم الصرفة / قسم الرياضيات 11 ( رياضيات ) 20
2
Find the solution set of the following inequalities
In other words :? Find the value of x which satisfy the following inequalities :
1- 2x ? 21< 27 + 4x
Solution:? ? 27 ? 21< ?2x + 4x ? ? 48 < 2x ??24 < x
The solution set x > ?24
2- x2 ? x ?12 < 0
Solution:?
x2 ? x ?12 < 0 ? (x ? 4)(x + 3) < 0
The solution set is ? 3 < x < 4
3- 2x2 + 5x + 2 > 0
Solution:?
2x2 +5x +2 > 0 ? (2x +1)(x + 2) > 0
The solution is
2
x < ?2 or x > ? 1
4- x3 ? x < 0
Solution:?
x(x2 ?1)<0 ? x(x ?1)(x +1) < 0
The solution set is x < ?1 or 0 > x <1
5- 0
6
1
2 <
+ ?
?
x x
x
Solution:? 0
( 3)( 2)
1 <
+ ?
?
x x
x
The solution set is x < ?3 or 1< x < 2
جامعة بابل / كلية التربية للعلوم الصرفة / قسم الرياضيات 11 ( رياضيات ) 20
3
Solve the following inequalities and show their solution sets on the real line.
Solution