Express the interval in terms of an inequality involving absolute

tebollahb

tebollahb

Answered question

2021-12-06

Express the interval in terms of an inequality involving absolute value. (-2.4, 1.9)

Answer & Explanation

Samantha Brown

Samantha Brown

Beginner2021-12-07Added 35 answers

Step 1
We know that the open intervals (a, b) can be expressed as an inequality with absolute value representing the interval as,
{xR:|xc|<r}. Here, c=a+b2 and r=ba2 is the radius of the interval.
Step 2
The given interval is (−2.4, 1.9).
So, a=−2.4, b=1.9.
The midpoint of the interval,
c=a+b2
=2.4+1.92
=-0.25
The radius of the interval is given by,
r=ba2
=1.9(2.4)2
=1.9+2.42
=4.32
=2.15
Hence the required inequality is |x−(−0.25)|<2.15
That is, |x+0.25|<2.15.

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