Linear and Quadratic Functions: Solving Linear Equations and Inequalities

think icon Think & Click: Compound Inequalities

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

Solve and graph 2 – n > 2 and -4n + 1 ≤ 21.
 

2 – n > 2
2 – 2 – n > 2 – 2
-n > 0
n < 0

and

-4n + 1 ≤ 21
-4n + 1 – 1 ≤ 21 – 1
-4n ≤ 20
n ≥ -5

n ≥ -5 and n < 0

Solution to Self Check
 
Solve 2x + 6.4 ≤ 12 or 2x + 4 ≥ -8.2
 

2x + 6.4 ≤ 12
2x + 6.4 – 6.4 ≤ 12 – 6.4
2x ≤ 5.6
x ≤ 2.8

or

2x + 4 ≥ -8.2
2x + 4 – 4 ≥ -8.2 – 4
2x ≥ -12.2
x ≥ -6.1

Since this an "or" statement, these two inequalities will cover the whole number line. Therefore the answer is All Real Numbers.