Worked example 1
Solve x + 8 = 15.
To isolate the variable, subtract 8 from both sides: x + 8 - 8 = 15 - 8, so x = 7. Check: 7 + 8 = 15. ✓
Answer: x = 7
Grade 6 Math · Topic 48
Solving One-Step Equations: Addition and Subtraction
To solve an equation, do the same operation to both sides until the variable is alone. For an equation like x + a = b, subtract a from both sides. For x - a = b, add a to both sides. Then check by plugging the answer back in.
Lesson alignment: 6.EE.B.5 · 6.EE.B.7 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Solve an addition or subtraction equation
The scale models equality. Use the inverse operation on both sides to isolate x.
Think first: What inverse operation will isolate x, and what must happen to both sides?
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.
Grade 6 core skill · 6.EE.B.5
Test a proposed solution by substitution
A solution is a value that makes the original equation true. Substitute the proposed value for the variable, then check whether both sides are equal.
Does x = 12 solve x + 7 = 19?
Replace x with 12: 12 + 7 = 19. The statement is true, so 12 is a solution.
12 + 7 = 19 ✓
Try x = 10: 10 + 7 = 17, and 17 ≠ 19. So 10 is not a solution.
Check in the original equation, not only in a rearranged line. For an inequality, the substituted value must make the inequality true.
Quick check: Is x = 6 a solution to 3x = 18?
Substitute: 3 × 6 = 18. Both sides match, so yes.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Solve y - 6 = 13.
Add 6 to both sides: y - 6 + 6 = 13 + 6, so y = 19. Check: 19 - 6 = 13. ✓
Answer: y = 19
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- x + 5 = 12
Check
x=7
- y + 9 = 17
Check
y=8
- a - 4 = 10
Check
a=14
- b - 7 = 3
Check
b=10
- x + 12 = 20
Check
x=8
- m - 15 = 5
Check
m=20
- n + 6 = 6
Check
n=0
- k - 9 = -2
Check
k=7
Try this situation 1
After spending $8, Carlos has $15 left. How much did he start with? (Let x be the starting amount.)
Show a worked solution
Answer: $23.
Start by writing the calculation clearly: x - 8 = 15 ⇒ x = 23.
Try this situation 2
A scout troop adds 5 new members and now has 22. Write and solve an equation for the original number m.
Show a worked solution
Answer: m = 17.
Start by writing the calculation clearly: m + 5 = 22 ⇒ m = 17.
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.