ACT Algebra Absolute Value

SAT Question of the Day

The SAT question of the day is an Identifying Sentence Errors Question that has already been addressed on this blog: click here to see an explanation.

ACT Math Question of the Day

What are the values of a and b, if any, where a|b – 2| < 0 ?

There are three things you must understand to solve this problem: number properties, absolute value, and inequalities.

Start by considering the equation as a whole. You know that the side that contains the variables must be less than zero. What kind of numbers are less than zero? Negative numbers! Now you know that a|b – 2| must be a negative number.

Break down a|b – 2| into its essential parts. It is really just the variable a multiplied by |b – 2|. What kinds of numbers do you have to multiply together in order to get a negative number? You must have a positive number times a negative number. You know that anything inside the absolute value bars will be positive. That is your positive number. Now you know that variable a must be negative! In other words a < 0!

Now that you know the restrictions on variable a, look at b. You know that you need a negative number times a positive number and it must be less than 0. Think about the properties of 0. Zero is neither negative nor positive. You must make sure that the second part of your equation (|b – 2|) does not equal 0. When does |b – 2| = 0? When b = 2. Therefore, for your equation to work, b ≠ 2.

A.a < 0 and b ≠ 2
B.a < 0 and b = 2
C.a ≠ 0 and b > 2
D.a > 0 and b < 2
E. There are no such values of a and b.

The correct answer is (A).

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