The absolute value of a, decreased by 22

Question

Translate the phrase to an algebraic expression. If no variable is given, use xas the variable. See Example 3.The absolute value of a, decreased by 22

Answer 1

It seem that there is more to the problem with the "use x as the variable" directions.  The absolute value of an expression is a function that "wipes away" the sign.  It represents the distance from zero.

The absolute value of a => |a| in symbols

decreased by 22 => subtract 22

Puting these together you get:  |a| - 22

For example, given a=-2, |a| - 22 = |-2| - 22 = 2 - 22 = -20.

If the sentence was "The absolute value of A decreased by 22" a better translation would be => |A - 22|

The use of the comma in the sentence implies that A is not decreased by 22 before the absolute value is applied.