Worked example 1
Solve x + 5 < 12.
To isolate the variable, subtract 5 from both sides: x < 7. Graph: open circle at 7, shade left. Check x = 0: 0 + 5 = 5 < 12. ✓
Answer: x < 7
Grade 6 Math · Topic 51
Solving One-Step Inequalities
Solving one-step inequalities works just like solving one-step equations: do the same operation to both sides until the variable is alone. The only twist (which you'll meet later in middle school) is multiplying or dividing by a negative flips the inequality. With positive numbers in this lesson, the inequality stays the same.
Lesson alignment: 6.EE.B.8 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Show which values solve the inequality
An open circle leaves out the boundary; a closed circle includes it.
Think first: Which direction should include the values that make this inequality true?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Solve 4x ≥ 20.
To keep the equation balanced, divide both sides by 4: x ≥ 5. Graph: closed circle at 5, shade right.
Answer: x ≥ 5
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- x + 4 > 9
Check
x>5
- y - 6 ≤ 2
Check
y≤ 8
- 3a < 15
Check
a<5
- (m)/2 ≥ 8
Check
m≥ 16
- x + 7 ≤ 12
Check
x≤ 5
- 5b > 35
Check
b>7
- n - 9 < 1
Check
n<10
- (k)/4 ≤ 6
Check
k≤ 24
Try this situation 1
Anna needs more than $30 to buy a gift. She has $x. Write and solve an inequality if she also gets $12 from her brother.
Show a worked solution
Answer: x > 18.
Start by writing the calculation clearly: x + 12 > 30 ⇒ x > 18.
Try this situation 2
A team can have at most 24 players. Coaches form 3 equal-sized squads of s players each. Write and solve an inequality for s.
Show a worked solution
Answer: s ≤ 8.
Start by writing the calculation clearly: 3s ≤ 24 ⇒ s ≤ 8.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.