 # Express the interval in terms of an inequality involving absolute value. (0,4) Kyran Hudson 2021-02-22 Answered
Express the interval in terms of an inequality involving absolute value.
(0,4)
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Step 1
To express the given interval in terms of an inequality involving absolute value.
Step 2
Given information:
The interval is (0, 4).
Step 3
Calculation:
Let (a, b) is an open interval and r is the radius, and the midpoint is c, then the interval can be represented as
$\left\{x\in R|x-c\mid
where $c=\frac{a+b}{2}$ and $r=\frac{b-a}{2}$
And the given interval is (0, 4).
So, midpoint is
$c=\frac{a+b}{2}$
$c=\frac{0+4}{2}$
$c=\frac{4}{2}$
$c=2$
$r=\frac{b-a}{2}$
$r=\frac{4-0}{2}$
$r=\frac{4}{2}$
$r=2$
Step 4
So, the inequality involving absolute value will be
$\left\{x\in R|x-c\mid
$\left\{x\in R|x-2\mid <2\right\}$
Thus, the inequality is $\left\{x\in R|x-2\mid <2\right\}$

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