330 algebra De mystif ieD
EXAMPLE
37 < ≤ x (, 37 ]
–≤ 41 ≤x – [–4, –1]
–8 < <x 8 (–8, 8)
0 ≤ x < 21 [, 0 )^1
2
–6 < <x 0 (–6, 0)PRACTICE
Give the interval notation for the double inequality.- 6 < x < 8
- –4 ≤ x < 5
- –2 ≤x < 2
- 0 ≤ x ≤ 10
- 9 < x< 11
6.^14 ≤ x ≤ 21 - 904 < x < 1100
✔SOLUTIONS
- 6 < x < 8 (6, 8)
- − 4 ≤ x < 5 [−4, 5)
- − 2 ≤ x < 2 [−2, 2)
- 0 ≤ x ≤ 10 [0, 10]
- 9 < x ≤ 11 (9, 11]
- 41 ≤ ≤ x 21 41 , 21
- 904 < x < 1100 (904, 1100)
Solving Double Inequalities
We solve double inequalities the same way we solve other inequalities except
that there are three “sides” to the inequality instead of two.EXAMPLE
Solve the double inequality and give the solution in interval notation.
4 ≤ 2x ≤ 12EXAMPLEPRACTICE
Give the interval notation for the double inequality.EXAMPLE
Solve the double inequality and give the solution in interval notation.