Interpret solution sets, test values in inequalities, and solve
one-step inequalities.
6.EE.B.5 · 6.EE.B.8 · Equations & Inequalities
Level
Guided practice with vocabulary support
🟠 Level 0 — Extra Support
Watch first: the worked example and hints are already shown for you.
One at a time: answer one question, check it, then go on.
Read aloud: press 🔊 Read aloud, then click any sentence to hear it.
Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W
Warm-Up
2 questions
Warm-Up 1
Which symbol means "less than or equal to"?
Vocabulary: Inequality symbols compare two values.
< means less than.
> means greater than.
≤ means less than or equal to.
≥ means greater than or equal to.
✓Correct! The symbol ≤ means "less than or equal to." It includes
the value itself and everything smaller.
✗Not quite. The symbol ≤ means "less than or equal to." The line
under the angle means "or equal to." The answer is
C.
Warm-Up 2
True or false: The number 5 is a solution to the inequality
x > 3.
Hint: To test a value,
replace x with 5 and check: is 5 > 3?
✓Correct! Substitute 5 for x: 5 > 3 is true, so 5 is a
solution.
✗Replace x with 5: is 5 > 3? Yes, 5 is greater than 3, so the
statement is true.
P
Practice
5 questions
Practice 1
Which of the following values is a solution to
n + 3 > 7?
Strategy: Replace n with each value and add
3. Which result is greater than 7? Test a value: substitute, compute, then
compare.
Explain how you tested the values:
Sentence frame: "I replaced n with ___. ___ + 3 = ___. Since ___ is
greater than 7, n = ___ is a solution."
✓Correct! 5 + 3 = 8, and 8 > 7 is true. So n = 5 is a solution to
n + 3 > 7.
✗Test each value: 5 + 3 = 8, and 8 > 7 is true. The answer is
C, n = 5.
Practice 2
True or false: The inequality
x < 10 has exactly 5 solutions.
Key idea: An inequality like x < 10 has
infinite solutions — not just whole
numbers. Values like 9, 8.5, 0, −3, and 9.999 all work. There is
no limit to how many numbers are less than 10.
Explain why the inequality does or does not have exactly 5
solutions:
Sentence frame: "The inequality x < 10 does not have exactly 5
solutions because ___. It has ___ solutions."
✓Correct! The inequality x < 10 has infinitely many solutions.
Any number less than 10 — including fractions and decimals
— is a solution.
✗An inequality like x < 10 does not have just 5 solutions. It has
infinitely many solutions: 9, 8, 7.5, 0,
−100, and so on. The answer is false.
Practice 3
Solve each inequality. Write the solution.
How to solve: Use inverse operations, just like
equations. To undo "+ 3", subtract 3 from both sides. To undo "×
2", divide both sides by 2. The inequality sign stays the same
direction. Boundary value: the number where the
inequality changes from true to false.
a. x + 3 > 7 → x
>
b. 2n ≤ 12 → n
≤
c. y − 5 ≥ 10 →
y ≥
Sentence frame: "To solve ___, I ___ both sides by ___. The solution
is ___."
✓All correct! x > 4, n ≤ 6, and y ≥ 15. Great work using
inverse operations.
✗Some answers need another look. Use inverse operations: subtract 3
from both sides of x + 3 > 7, divide both sides of 2n ≤ 12 by
2, and add 5 to both sides of y − 5 ≥ 10.
Practice 4
Sort each value into the correct category: Does it satisfy the
inequality m + 2 ≤ 8?
Step-by-step:Solution set = all values that make the
inequality true. First solve: m + 2 ≤ 8, so m ≤ 6. Then check
each value: is it ≤ 6?
m = 3
m = 9
m = 6
m = 7
m = 0
m = 10
Solution (m ≤ 6)
Not a Solution
Explain how you decided which values belong in each group:
✓All correct! Since m ≤ 6, the values 0, 3, and 6 satisfy the
inequality. Values 7, 9, and 10 do not.
✗Some items are in the wrong group. Solve first: m + 2 ≤ 8 means
m ≤ 6. Any value 6 or less is a solution. Try again!
Practice 5
A roller coaster requires riders to be at least 48 inches tall. This
can be written as h ≥ 48. Which
statement best describes the solution set?
Vocabulary: The
solution set is the collection of all
values that make an inequality true. "At least 48" means 48
and anything greater. Hint: Think about the
boundary value (48). Is 48 itself included?
Explain what the solution set means in this situation:
Sentence frame: "The solution set h ≥ 48 means that any height
that is ___ or ___ is allowed on the ride."
✓Correct! h ≥ 48 means all heights that are 48 inches or greater.
The ≥ symbol includes the boundary value 48.
✗The symbol ≥ means "greater than or equal to," so 48 is
included. The solution set is all heights that are 48 inches or
greater. The answer is C.
★
Challenge
1 question
Challenge
A bag can hold at most 25 pounds. You already packed
11 pounds. Write and solve an inequality for how much more weight,
w, you can add. Then explain what the
solution set means in this situation.
Think about it: "At most 25 pounds" means the total
weight must be ≤ 25. The total is 11 +
w. So write: 11 + w ≤ 25. Now solve for w by subtracting 11 from
both sides.
Your inequality:
Solve it (what is w?):
Explain what the solution set means in this situation:
Sentence frame: "The inequality is ___. I subtracted ___ from both
sides to get w ≤ ___. This means you can add ___ pounds or less
to the bag."