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Chapter 1: Q51. (page 31)

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

If aand b,creal numbers, then c|a+b|=|ca|+|cb|.

Short Answer

Expert verified

The statement is always true.

Step by step solution

01

Step 1- Consider the statement.

Consider the statement c|a+b|=|ca|+|cb|.

02

Step 2- Step description.

Let a=5,b=3,c=2.

Substitute the values a=5,b=3,c=2in the equation c|a+b|=|ca|+|cb|and simplify.

c|a+b|=|ca|+|cb|2|5+3|=|(2)5|+|(2)3|2|8|=|10|+|6|2(8)=10+616=16

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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