Lesson 8.2Write and Solve Equations Using Addition or Subtraction
Start hereWords, worked example, and sentence starters
Learning target I can solve one-step addition and subtraction equations using inverse operations.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| EquationSpanish: Ecuación | A math sentence with an equal sign showing both sides are the same. | x + 25 = 60 — both sides equal 60 when x = 35 |
| Inverse operationSpanish: Operación inversa | Two math actions that undo each other, like × and ÷. | + and − |
| IsolateSpanish: Despejar | To get the letter by itself on one side. | get x by itself |
| SolutionSpanish: Solución | A number that makes the equation or inequality true. | x = 7 is the solution to x + 5 = 12 because 7 + 5 = 12 ✓ |
| One-step equationSpanish: Ecuación de un paso | An equation you can solve in a single step using one inverse operation. | x + 7 = 20 |
| BalanceSpanish: Equilibrio | Keeping both sides of an equation equal by doing the same thing to each side. | do the same to each side |
How it worksWorked examplesolving an addition equation
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A shop had x hats. After 17 hats were delivered, the shop had 45 hats. Solve x + 17 = 45.
- Look at the variable side: 17 is added to x, so the inverse move is subtraction.
- Subtract 17 from BOTH sides so the equation stays balanced.
- Left side: x + 17 − 17 leaves x. Right side: 45 − 17 gives 28.
- Check by substituting: 28 + 17 makes 45, so both sides agree.
Answer: x = 28, so the shop had 28 hats before the delivery.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Lin had n trading cards. After a swap brought 24 more, she had 51. Solve n + 24 = 51.
- What is done to n? is added, so the inverse operation is .
- Do the same to each side: subtract from both sides.
- Left side leaves . Right side: 51 − 24 = .
- Check: + 24 = . Does it balance?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The variable has added to it, so I from both sides.
- I must do the same thing to both sides because .
- My solution is , and my check shows .
- Addition and subtraction are inverse operations because .
Word bank equationvariableinverse operationsubtractisolatebalanceboth sidessolutioncheckundoProperty of Equality
Watch outA common mistake
A common mistake is applying the same operation instead of the inverse — for example, solving x − 7 = 15 by subtracting 7 from both sides (getting the wrong x = 8) instead of adding 7 to both sides (the correct x = 22). Another common mistake is doing the inverse operation to only one side, like solving x + 6 = 14 by subtracting 6 from the left but forgetting the right side. Before you submit, name the operation shown in the equation, choose its inverse, apply it to BOTH sides, and check by substituting your answer back into the original equation.
Lesson 8.2Write and Solve Equations Using Addition or Subtraction
Version ASupported practice
Learning target I can solve one-step addition and subtraction equations using inverse operations.
-
1Mark and label each value on the number line.
Use the number line to solve x + 8 = 20. Start at 20 and count back 8 to find x.
Hint Start at 20 on the number line. Since x + 8 = 20, subtract 8 to find x.
Show your thinking
-
2Circle the letter of the best answer. Show how you know.
Solve: x + 9 = 15
- Ax = 6
- Bx = 9
- Cx = 15
- Dx = 24
Hint x has 9 added to it. To get x alone, you need to UNDO that addition.
Show your work -
3Circle the letter of the best answer. Show how you know.
Solve: y − 7 = 20
- Ay = 7
- By = 13
- Cy = 27
- Dy = 140
Hint Look at what's happening to y: 7 is being SUBTRACTED. Which operation undoes subtraction?
Show your work -
4Circle the letter of the best answer. Show how you know.
Solve: n + 15 = 42
- An = 15
- Bn = 27
- Cn = 42
- Dn = 57
Hint n is being increased by 15. To find n alone, you must undo that addition.
Show your work -
5Circle the letter of the best answer. Show how you know.
Solve: m − 11 = 25
- Am = 14
- Bm = 25
- Cm = 36
- Dm = 275
Hint m has 11 taken away from it. Think about which operation puts that 11 back.
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1Equationx + 6 = 14
- 2Choose inverseThe inverse of + 6 is − 6.
- 3Subtract from one side onlyx + 6 − 6 = 14, so x = 14
Which step has the mistake? Explain what went wrong, then show the correct work.
Hint Step 3 only subtracted 6 from the left side. What happened to the right side?
Correct workCorrect answer:
Explain your thinkingWhy do you have to subtract 19 from BOTH sides, not just one?
Sentence starter I subtract from both sides because an equation is like a ___ — to keep it balanced, any operation on one side must ___.
Lesson 8.2Write and Solve Equations Using Addition or Subtraction
Version BCore practice
Learning target I can solve one-step addition and subtraction equations using inverse operations.
-
1Decide whether each pair balances. Check Yes or No, then explain.
Solve: m − 14 = 32
Left side Right side Balanced? Explain your choice -
2Complete the table. Show how you found each value.
Complete the table: identify the inverse operation, solve, and check.
Equation Inverse Operation Solution Check x + 18 = 45 p − 22 = 19 w + 3.5 = 10 Show your work -
3Write the name of the correct group on each line.
Sort each equation by the inverse operation needed to solve it.
- x − 9 = 14
- n − 20 = 35
- y − 6 = 8
- x + 12 = 30
- n + 7 = 19
- y + 15 = 40
-
4Circle the letter of the best answer. Show how you know.
A shirt costs $d. After a $15 discount, it costs $38. What is d?
- A$23
- B$38
- C$45
- D$53
Show your work
-
5Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1Equationy − 13 = 28
- 2Choose inverseThe inverse of − 13 is + 13, so add 13 to both sides.
- 3Apply to both sidesy = 28 + 13
- 4Simplifyy = 31
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhy do you have to subtract 19 from BOTH sides, not just one?
Lesson 8.2Write and Solve Equations Using Addition or Subtraction
ChallengeExtension
Learning target I can solve one-step addition and subtraction equations using inverse operations.
-
1Decide whether each pair balances. Check Yes or No, then explain.
Solve using decimals: x + 2.7 = 9.3. Use inverse operations.
Left side Right side Balanced? Explain your choice
-
2Find the mistake. Explain it, then show the correct work.
Find the Equation Error
- 1Equationx − 18 = 45
- 2Identify inverseInverse of subtraction is subtraction
- 3Apply to both sidesx − 18 − 18 = 45 − 18
- 4Simplifyx = 27
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
A detective solved x + 25 = 60 and got x = 35. Another detective solved y − 25 = 60 and got y = 35. Are both correct? Explain using inverse operations and check each answer.
Write your answer