In ABC, AB = 5 feet and BC = 3 feet.
Which inequality represent all possible values for the length of AC, in feet?
1. 2 <_AC <_ 8
2. 2 < AC < 8
3. 3 <_ AC<_ 7
4. 3 < AC <7

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

As per the law of triangle inequality, the sum of any two sides of the triangle must be greater than or equal to the third side, this will give three conditions,

5+3 ≥ AC ⇒ 8 ≥ AC
AC + 3 ≥ 5 ⇒ AC ≥ 2
AC + 5 ≥ 3

Since the third condition is going to be true for all the whole numbers. Therefore, as per the first two conditions, the value of AC should be 2≤AC≤8.

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In ABC, AB = 5 feet and BC = 3 feet. Which inequality represent all possible values for the length of AC, in feet? 1. 2 <_AC <_ 8 2. 2 < AC < 8 3. 3 <_ AC<_ 7 4. 3 < AC <7

Answer :

What are inequalities?

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In ABC, AB = 5 feet and BC = 3 feet.
Which inequality represent all possible values for the length of AC, in feet?
1. 2 <_AC <_ 8
2. 2 < AC < 8
3. 3 <_ AC<_ 7
4. 3 < AC <7