WOLFRAM|DEMONSTRATIONS PROJECT

Inequalities and Equations with Absolute Values

​
choose relation
=
>
≥
<
≤
+
-
a
1
b
-1
c
-1
d
2
e
-3
f
-5
show division of R
eliminate absolute value
reduce left side
show (particular) solutions
overall/conditional
show solution
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x
7
y
12
Solve the inequality:
x-1 - 2-x ≥ -3x-5
x ≤ 1
(-(x-1)) - (2-x) ≥ -3x-5
-1≥-3x-5
x≥-
4
3
1 < x ≤ 2
(x-1) - (2-x) ≥ -3x-5
2x-3≥-3x-5
x≥-
2
5
x > 2
(x-1) - (-(2-x)) ≥ -3x-5
1≥-3x-5
x≥-2
Solution:
x≥-
4
3
This Demonstration solves relations of the form
ax+b±cx+d>ex+f
. The "greater than" sign
>
can also be changed to
=
,
≥
,
<
, or
≤
.