7.2 Writing Two-Step
Inequalities
Essential Question: How do you write a two step
inequality?
Objective: SWBAT write and solve a two step
inequality.
Inequality Rules
CASE STUDY
3x + 5 ≥ 20
-5 -5
Subtract 5 from both sides
3x ≥ 15
/3
/3
Divide both sides by 3
Solution: x ≥ 5
Check:
3(6) + 5 ≥ 20
18 + 5 ≥ 20
23 ≥ 20
True.
-2k + 5 ≥ -3
-5 -5
Subtract 5 from both sides
-2k ≥ -8
/-2 /-2
Divide both sides by -2
Flip the sign
Solution: k ≤ 4
Check:
-2(2) + 5 ≥ -3
-4 + 5 ≥ -3
1 ≥ -3
True
Example Two
A mountain climbing team is camped at an altitude of 18,460 feet on Mount Everest. The
team wants to reach the 29,029 foot summit within 6 days. Write an inequality to find the
average number of feet per day the team must climb to accomplish its objective.
Step 1: What is it that you are trying to find? This will be your variable.
Step 2: What is it your problem must equal, be less than, or be greater than?
Step 3: Identify important information in the problem you will need.
Step 4: Put it all together.
Example Three
Write a word problem to represent 2x + 20 ≤ 50.
Step 1: Analyze what each part of the inequality means mathematically.
Step 2: Create a story that matches each operation.