Description:
Inequality questions require you to solve equations with any of
the four inequality symbols:
>,
<,
≥,
or ≤
Approach:
Treat these problems just like any other algebra problem by doing
the exact same thing to both sides of the equation until you have the desired
variable isolated. Remember to switch the inequality symbol when you multiply
or divide by a negative number. Additionally, when an absolute value symbol
is combined within an inequality, you must solve two equations.
1) Basic Inequalities
Solve basic inequalities in the same way that you solve algebraic
equations.
For example:
x + 6 < 13; therefore, x = 7
If you need to multiply or divide by -1, switch the inequality sign.
-
5 - y > 2
-
therefore, -y > -3
-
therefore, y < 3
1-1. Practice:
-
2x - 7 > 15
-
14 - 2r ≥ 28
-
y + 8 < 12
2) Absolute Value Inequalities
Absolute value inequalities require special treatment.
For example:
If | x + 7 | < 2, what are
the possible values of x?
We must translate and solve this problem in two ways:
-
Drop the absolute value signs and solve the inequality as usual.
-
x + 7 < 2; therefore, x < -5
-
Drop the absolute value signs, switch the direction of the
inequality symbol, and make the right side of the equation negative.
-
x + 7 > -2; therefore, x > -9
Therefore, the solution to this problem is
-9 < x < -5
2-1. Practice:
-
If | x - 12 | = 20, what are the possible values of x?
-
If | 7 - y | = 13, what are the possible values of y?
-
If | 2r - 8 | = 14, what are the possible values of r?
