Double inequalities are used to solve word problems where the solution is a limited range of values. Usually there are two variables and you are given the range of one of them and asked to find the range of the other.
Examples
y = 3x – 2
If 7 ≤ y ≤ 10,
what is the corresponding interval for x?
Because y =
3x – 2, replace ‘‘y’’ with ‘‘3x – 2.’’
y = 4x + 1
If –3 < y
< 3, the corresponding interval for x can be found by solving –3 < 4x + 1
< 3.
y = 3 – x
If 0 ≤ y
< 4, the corresponding interval for x can be found by solving 0 ≤ 3 – x <
4.
Practice
Give the
corresponding interval for x.
Solutions
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Mathematician
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