PE 1 - Inequalities & Modulus | Algebra - Inequalities & Modulus
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For two real numbers a and b, let x = |a| + |b|, y = |a| − |b|, and z = |a − b|. Which of the following is true?
- (a)
z ≤ x ≤ y
- (b)
x ≤ y ≤ z
- (c)
y ≤ z ≤ x
- (d)
y ≤ x ≤ z
Solution
Discuss
ReportThe range of f(x) = |x| + |x – 3| + |x + 5| is?
- (a)
[–5, 3]
- (b)
[0, 5]
- (c)
[11, ∞)
- (d)
[8, ∞)
The solution set for the inequation |x − 2| + |x + 3| < 2 is _______.
- (a)
(−∞,−2) ∪ (1, ∞)
- (b)
[2, 1)
- (c)
(−1, 2)
- (d)
an empty set
If x, y and z are positive real numbers such that x + y + z = 5, then which of the following is always true?
- (a)
xyz ≤ 5/3
- (b)
xyz ≥ 5/3
- (c)
xyz ≤ 125/27
- (d)
xyz ≥ 27/125
What is minimum value of , , , where x, y and z are positive real numbers.
- (a)
3
- (b)
6
- (c)
0
- (d)
1
What is minimum value of + + , where x, y and z are positive real numbers
- (a)
3
- (b)
6
- (c)
0
- (d)
1
If x and y are positive real numbers and x3y2 = 48, then the minimum value of 2x + 3y is?
- (a)
10
- (b)
14
- (c)
24
- (d)
Cannot be determined
Find the number of solutions of the equation 2x2 + |4x - 7| = 9