To solve and graph an inequality, you test numbers to see which make it true, then place them on a number line — that runs on substituting to check and number line basics. Warm up both and this lesson clicks.
Answer these 3, then press Show my path. No grade — this just points you to the right level.
1. Does x = 5 make x > 3 true?
2. Which number is a solution of n < 4?
3. Numbers get bigger as you move which way on a number line?
A number is a solution of an inequality if it makes the inequality true when you substitute it in. Many numbers can work. Then you show all of them on a number line.
Your quick check picks one for you, but you can switch any time:
Level 0 Substitute and decide true or false.
A. Is 7 > 2 true?
7 is bigger than 2, so 7 > 2 is true.
B. Is 3 < 1 true?
3 is bigger than 1, so 3 < 1 is false.
C. Put x = 4 into x < 6. Is it true?
4 is smaller than 6, so 4 < 6 is true.
Level 1 Find a solution.
A. Which number is a solution of n > 5?
8 > 5 is true; 5 is not greater than itself, and 2 is too small.
B. Which number is a solution of n < 3?
1 < 3 is true; 3 is not less than itself, and 5 is too big.
Level 2 Test the boundary number.
A. Is 2 a solution of n > 2?
n > 2 needs a number bigger than 2; 2 equals 2, so it does not count.
B. "At least 5" means a number that is…
"At least 5" includes 5 and every number above it.
1. Which number is a solution of n > 6?
9 > 6 is true; 6 is not greater than itself.
2. Is x = 3 a solution of x < 3?
x < 3 needs a number smaller than 3; 3 equals 3, so it does not count.
You've practiced exactly what Lesson 7-6 uses. Time to dive in.
Start Lesson 7-6 →