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Chapter 2: Problem 77

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(y-a=-b,\) then \(y=a+b\)

Short Answer

Expert verified
The statement 'If \(y - a = -b\), then \(y = a + b\)' is False. The correct statement should be 'If \(y - a = -b\), then \(y = a - b\)'.

Step by step solution

01

Inspect the initial equation

We're given that \(y-a = -b\). By adding \(a\) on both sides of the equation, we can isolate \(y\).
02

Add 'a' on both sides

Perform the operation of adding \(a\) to both sides of the equation, yielding: \(y = a - b\).
03

Compare with the given statement

By comparing with the statement 'if \(y-a = -b\), then \(y = a+b\)', we can see that it's a false statement. Because the right side of the resulting equation and the one provided in the statement are different.
04

Correct the false statement

So, correcting the statement, it should be 'If \(y - a = -b\), then \(y = a - b\)'.

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