SOLVING INEQUALITIES INVOLVING QUADRATICS WORKSHEET
Show on a number line the solutions to :
Problem 1 :
x2 ≥ 16
Problem 2 :
x2 < 25
Problem 3 :
x2 < 1
Problem 4 :
x2 ≥ 4
Problem 5 :
x2 ≥ 25
Problem 6 :
x2 < 49
Problem 7 :
x2 > 4
Problem 8 :
x2 ≥ 6.25
Problem 9 :
x2 < 0.25
Problem 10 :
x2 ≥ 2.25
Answer Key
1) x ≤ -4 or x ≥ 4
2) -5 < x < 5
3) -1 < x < 1
4) x ≤ -2 or x ≥ 2
5) x ≤ -5 or x ≥ 5
6) -7 < x < 7
7) -2 < x < 2
8) x ≤ -2.5 or x ≥ 2.5
9) -0.5 < x < 0.5
10) x ≤ -1.5 or x ≥ 1.5
Find the solutions of the following inequalities :
Problem 1 :
x2 + 6 ≥ 22
Problem 2 :
3x2 - 4 ≥ 8
Problem 3 :
5x2 - 20 < 105
Problem 4 :
4x2 < 1
Problem 5 :
9x2 ≥ 4
Problem 6 :
25x2 - 2 ≥ 2
Problem 7 :
36x2 + 7 ≤ 11
Problem 8 :
2(x2 – 5) < 8
Problem 9 :
(x2 + 6)/2 ≥ 53
Problem 10 :
10 - x2 > 6
Answer Key
1) So, the solution is (-∞, -4] and [4, ∞).
2) So, the solution is (-∞, -2] and [2, ∞).
3) So, the solution is (-5, 5)
4) So, the solution is (-1/2, 1/2)
5) So, the solution is (-∞, -2/3] and [2/3, ∞)
6) So, the solution is (-∞, -2/5] and [2/5, ∞)
7) So, the solution is [-1/3, 1/3]
8) So, the solution is (-3, 3)
9) So, the solution is (-10, 10)
10) So, the solution is (-2, 2)
11) So, the solution is (-∞, -3) and (3, ∞).
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