Lesson 15
Efficiently Solving Inequalities
Let’s solve more complicated inequalities.
Problem 1
 Consider the inequality \(\text1 \leq \frac{x}{2}\).
 Predict which values of \(x\) will make the inequality true.
 Complete the table to check your prediction.
\(x\) 4 3 2 1 0 1 2 3 4 \(\frac{x}{2}\)
 Consider the inequality \(1 \leq \frac {\text{}x}{2}\).
 Predict which values of \(x\) will make it true.
 Complete the table to check your prediction.
\(x\) 4 3 2 1 0 1 2 3 4 \(\text\frac{x}{2}\)
Problem 2
Diego is solving the inequality \(1003x \ge \text50\). He solves the equation \(1003x = \text50\) and gets \(x=50\). What is the solution to the inequality?
A:
\(x < 50\)
B:
\(x \le 50\)
C:
\(x > 50\)
D:
\(x \ge 50\)
Problem 3
Solve the inequality \(\text5(x1)>\text40\), and graph the solution on a number line.
Problem 4
Select all values of \(x\) that make the inequality \(\textx+6\ge10\) true.
A:
3.9
B:
4
C:
4.01
D:
4
E:
4.01
F:
3.9
G:
0
H:
(From Unit 6, Lesson 13.)
7
Problem 5
Draw the solution set for each of the following inequalities.

\(x>7\)

\(x\geq\text4.2\)
Problem 6
The price of a pair of earrings is $22 but Priya buys them on sale for $13.20.
 By how much was the price discounted?
 What was the percentage of the discount?