WOLFRAM|DEMONSTRATIONS PROJECT

Inequalities and Equations with Nested Absolute Values

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choose relation
=
>
≥
<
≤
a
1
b
-1
c
-2
d
-5
e
1
f
6
show division of R
eliminate inner | |
reduce left side
zeros of left side
part A
part B
show solution
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x
7
y
12
Solve the inequality:
x-1 + -2x-5 > x+6
A
B
A:
x≤-6
-x-6>x+6
x<-6
x<-6
-6<x≤-
5
2
x+6>x+6
False
False
B:
-
5
2
<x≤-
4
3
-3x-4>x+6
x<-
5
2
False
-
4
3
<x
3x+4>x+6
x>1
x>1
solution:
This Demonstration solves relations of the form
ax+b+cx+d>ex+f
, where
c≠0
and
c≠a
. You can change the greater than sign to =, ≤ , ≥, or <.