Find the value of inequality |x-1|-3x/x-4<=1/2
Answers
Step-by-step explanation:
How do you solve the inequality
1
x
+
1
>
3
x
−
2
?
Algebra Multi-Step Inequalities
2 Answers
Lotusbluete
Jan 19, 2016
x
<
−
5
2
×
or
×
−
1
<
x
<
2
Explanation:
First of all, note that your inequality is only defined if your denominators are not equal to zero:
x
+
1
≠
0
⇔
x
≠
−
1
x
−
2
≠
0
⇔
x
≠
2
Now, your next step would be to "get rid" of the fractions. This can be done if multiplying both sides of the inequality with
x
+
1
and
x
−
2
.
However, you need to be careful since if you multiply an inequality with a negative number, you must flip the inequality sign.
=========================================
Let's consider the different cases:
case 1:
×
x
x
>
2
:
Both
x
+
1
>
0
and
x
−
2
>
0
hold. Thus, you get:
x
−
2
>
3
(
x
+
1
)
x
−
2
>
3
x
+
3
... compute
−
3
x
and
+
2
on both sides...
−
2
x
>
5
... divide by
−
2
on both sides. As
−
2
is a negative number, you must flip the inequality sign...
x
<
−
5
2
However, there is no
x
that satisfies both the condition
x
>
2
and
x
<
−
5
2
. Thus, there is no solution in this case.
=========================================