Exercise series on absolute value
Exercise 1:
Solve in the following equations and inequations:
a) | 2 – x | < 4
b) | 6 – 2 x | = 3
c) | x + 2 | > 3
d) | x + 2 | < | x + 3 |
e) | x3 – 1 | + p > 0
f) 3 < | x + 2 | < 4
g) | 4 x²– 12 x + 9 | = 4
h) | 3 x + 1 | + | 1 – x | > 3
i) | 1 + x²| =2x
Exercise 2:
Calculate.
a) b)
c)
d) e)
f)
Exercise 3:
Without a calculator, simplify :
a) b)
c) d)
Exercise 4:
1.a) On a graduated line, place the numbers 5 and .
b) Calculate the distance between 5 and .
2. Repeat question 1. with 3 and .
3. Repeat question 1. with -1 and .
Exercise 5:
Using an absolute value, write the distance between :
a) and 2. b)
and 5
c) – 5 and d)
and 4
Exercise 6:
without calculator, simplify :
a) b)
c)
d) e)
f)
Exercise 7:
In the same way that represents the distance between the real number
and 3,
express in terms of distance :
a) b)
c) d)
e) f)
Exercise 8:
Determine the set, in interval form, of real numbers verifying :
a) b)
c)
Exercise 9:
Consider an interval [a ; b] with a and b two real numbers.
The center of the interval [a ; b] is the number
and radius of the interval [a ; b] the number .
Graphically, we have :
1. a) Calculate the center and radius of [2; 6].
b) Translate |x – 4| in terms of the distance between two real numbers.
c) Copy and complete:
2. In the same way, copy and complete :
a) .
b)
c)
Exercise 10:
Write an inequality verified by and using an absolute value in the following cases.
a) b)
a)
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