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Absolute Value Functions: Inequality with Absolute Values
Related Topics
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Absolute Value Functions
2 Activities
Find all
x
x
x
that satisfy the inequality
∣
x
2
−
3
x
+
1
∣
<
1
\left|x^2−3x+1\right|<1
x
2
−
3
x
+
1
<
1
x
∈
(
−
∞
,
0
)
∪
(
2
,
3
)
x∈(-\infty, 0)∪(2,3)
x
∈
(
−
∞
,
0
)
∪
(
2
,
3
)
x
∈
(
0
,
1
)
∪
(
2
,
3
)
x∈(0,1)∪(2,3)
x
∈
(
0
,
1
)
∪
(
2
,
3
)
x
∈
(
1
,
2
)
∪
(
3
,
∞
)
x∈(1,2)∪(3,\infty)
x
∈
(
1
,
2
)
∪
(
3
,
∞
)
x
∈
(
0
,
1
)
∪
(
2
,
3
)
x∈(0,1)∪(2,3)
x
∈
(
0
,
1
)
∪
(
2
,
3
)
I don't know
Check Submission
More Absolute Value Functions Questions:
Absolute Value Functions: Function Properties
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
, which of the following is true about
h
(
x
)
=
g
(
f
(
x
)
)
h\left(x\right)=g\left(f\left(x\right)\right)
h
(
x
)
=
g
(
f
(
x
)
)
?
Solve the following inequality
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
\left|2x-3\right|+\left|x-4\right|\ge3
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
Absolute Value Functions: Inequalities with Absolute Values
Solve the following inequality:
∣
x
+
1
∣
≥
x
+
4
2
\displaystyle\left|x+1\right|\ge\frac{x+4}{2}
∣
x
+
1
∣
≥
2
x
+
4
Absolute Value Functions: Function Properties
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
, which of the following is true about
h
(
x
)
=
g
(
f
(
x
)
)
h\left(x\right)=g\left(f\left(x\right)\right)
h
(
x
)
=
g
(
f
(
x
)
)
?
Absolute Value Functions
Solve the inequality for
x
x
x
,
∣
3
x
−
4
∣
+
∣
x
−
2
∣
≥
5
|3x-4|+|x-2| \geq 5
∣3
x
−
4∣
+
∣
x
−
2∣
≥
5
.
Solve the following inequality
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
\left|2x-3\right|+\left|x-4\right|\ge3
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
Absolute Value Functions: Inequalities with Absolute Values
Solve the following inequality:
∣
x
+
1
∣
≥
x
+
4
2
\displaystyle\left|x+1\right|\ge\frac{x+4}{2}
∣
x
+
1
∣
≥
2
x
+
4
Absolute Value Functions: Inequality with Absolute Values
Find all
x
x
x
that satisfy the inequality
∣
x
2
−
3
x
+
1
∣
<
1
\left|x^2−3x+1\right|<1
x
2
−
3
x
+
1
<
1