Page 205 - ABCTE Study Guide_Neat

Question

Solve

A h = 1 or h = -1

B h = 1 or h = -4

C h = -1 or h = 4

D h = 4 or h = -4

Answer

The correct answer is D. First, add 12 to both sides of the equation. Then you have |8h|= 32. This means
that hcan be either 4 or -4 in order to make the absolute value true.

Absolute-Value Inequalities

It would be nice if absolute-value inequalities were as easy to work with as absolute-value equations.
Alas, absolute-value inequalities are more complicated.

Absolute-value inequalities become compound inequalities. Compound inequalities are two inequalities
joined by AND or OR. In logic and math problems, AND means both or all parts are true. OR means that
one or the other part is true, but not necessarily both.

Example

Think of a number that is even AND greater than ten. Twelve works, eight does not. The number must
meet both criteria.

Think of a number that is even OR is greater than ten. Eight works, 12 works, and so does 15. The
number only needs to meet one of the two criteria, although it can meet both.

Absolute-value inequalities are best explained with the help of examples. Here are the most basic types of
inequality problems.