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Chapter 1: Q50. (page 30)

For the following statement, determine whether the statement is always, sometimes or never true. Explain your reasoning.

If aand breal numbers, then |a+b|=|a|+|b|.

Short Answer

Expert verified

The statement is always true.

Step by step solution

01

Step 1- Consider the statement.

Consider the statement |a+b|=|a|+|b|.

02

Step 2- Step description.

Let a=5,b=3.

Substitute the values a=5,b=3in the equation |a+b|=|a|+|b|and simplify.

|a+b|=|a|+|b||5+3|=|5|+|3||8|=5+38=8

03

Step 3- Step description.

Since the values are same on both the sides (L.H.S=R.H.S.) thus, the statement is always true.

Therefore, the statement is always true.

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