3.6 SAT Math - Inequalities

An inequality is solved just like an equation:

4a + 3 > 10
4a > 7
a > 7/4

The only differences between inequalities and regular equations are:

1) An inequality has a range of answers. So when you solve the equation 2p - 4 = 2 you get the answer p = 3. But when you solve the inequality 2p -4 < 2, your answer is p < 3, which means any number less than 3 is included in your answers. So could p be 0? Could p be - 1/3 ?   Yes to both.  Can p be 3?  NO, because the sign was “less than” not “less than or equal to.”

2) The most important thing to remember with inequalities is that, if you multiply or divide by a negative number, you must switch the direction of the sign.

2 - 4y < -6
-4y < -8
y > 2

-SAT Math Tip: Watch limits on numbers and inequalities.  In the following question, the limits given change the possible correct answers.

Example Inequality Problem

if x > 3 and 8/(x - 3) + 2 > 6, which of the following describes all possible values of x?

(A) x < 13/6
(B) 3 < x < 28/6
(C) x > 2
(D) x < 5
(E) 3 < x < 5

You can solve this sat math question just like an equation with an equals sign, except be careful of which answer choice you pick.  Once you do all the proper work, you should get x < 5, one of the answer choices.  But don’t pick it!  Check the limits first.  The question states that x > 3, which means that (E) is the better answer choice.

-SAT Math Tip:  Sometimes more than one answer choice will seem possible or correct.  Your job is to pick the BEST answer for any question, which means you need to use the information you were given to determine which answer BETTER satisfies the question than another.  Don’t panic if more than one seems correct – one will always be better than the other in the end.