Final answer:
If b is a rational number, and x + b is rational, x must also be a rational number.
Step-by-step explanation:
If b is a rational number, and x + b is rational, what must be true about x?
To determine what must be true about x, let's consider the given information:
If x + b is rational, it means that the sum of x and b is a rational number. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Since b is a rational number, it can be written as the quotient of two integers: b = p/q, where p and q are integers and q is not zero.
Now, let's substitute b in the expression x + b and simplify:
x + b = x + p/q
To have a rational sum, x must also be a rational number. This is because when a rational number is added to a rational number, the result is always a rational number.
Therefore, if x + b is rational, x must also be a rational number.