Exercise 54 Page 34

The absolute values of any real number and its opposite are always the same. The reason is that they are both an an equal distance from 0 on a number line. | a| = |- a| Therefore, the absolute value of a-b is equal to the absolute value of its opposite, which we can write as -(a-b). Let's distribute the negative sign and simplify the expression. Since b-a is the opposite of a-b, we get the following absolute value equation. |a-b|=|b-a| We can write a conclusion.

If a and b are real numbers, then |a-b| is always equal to |b-a|.