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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Expert Answer

Szeteib
Answered 2021-02-23 Author has 102 answers

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
{xR|xc<r}
where c=a+b2 and r=ba2
And the given interval is (0, 4).
So, midpoint is
c=a+b2
c=0+42
c=42
c=2
And radius is
r=ba2
r=402
r=42
r=2
Step 4
So, the inequality involving absolute value will be
{xR|xc<r}
{xR|x2<2}  [substitute values of r and c]
Thus, the inequality is {xR|x2<2}

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