Problem 77 - Introductory Algebra for College Students

Question

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 \(y=a+b\)

Step-by-Step Solution

Answer

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 1: Inspect the initial equation

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

Step 2: Add 'a' on both sides

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

Step 3: 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.

Step 4: Correct the false statement

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