Lesson 8-2: Write and Solve Equations Using Addition or Subtraction

Warm-Up 1

Which operation would you use to undo addition when solving an equation?

Vocabulary: An inverse operation is the opposite operation that undoes another. Addition and subtraction are inverse operations. To isolate the variable means to get it alone on one side of the equation.

✓Correct! Subtraction is the inverse operation of addition. To undo adding a number, you subtract the same number from both sides.

✗Not quite. Addition and subtraction are inverse operations. To undo addition, you subtract. The answer is C.

Warm-Up 2

True or false: The equation x + 5 = 12 and the equation 12 − 5 = x have the same solution.

Hint: Try solving both. For the first equation, subtract 5 from both sides. For the second, compute 12 − 5. Do you get the same value for x?

✓Correct! Both equations give x = 7. Subtracting 5 from both sides of x + 5 = 12 gives x = 7, and 12 − 5 = 7.

✗Actually, both equations have the same solution: x = 7. The statement is true.

Practice 1

Marcus had some baseball cards. He gave away 9 cards and now has 14 left. Which equation represents this situation?

Strategy: Let variable c stand for the number of cards Marcus started with. He gave away 9, so we subtract 9. He has 14 left.
Think: c − 9 = ?

Explain how you chose your equation:

Sentence frame: "Marcus started with ___ cards. He gave away ___, so I write ___ − ___ = ___."

✓Correct! "Gave away" means subtract. Marcus started with c cards, subtracted 9, and had 14 left: c − 9 = 14.

✗"Gave away" means subtraction. The unknown is how many he started with. The equation is B: c − 9 = 14.

Practice 2

Solve each equation. Write the value of the variable.

Steps to solve:
1. Look at the operation next to the variable.
2. Use the inverse operation on both sides.
3. Simplify to isolate the variable.

a. x + 7 = 15 → x =

b. n + 23 = 50 → n =

c. 34 + y = 61 → y =

Sentence frame: "To solve ___ + ___ = ___, I subtract ___ from both sides and get ___ = ___."

✓All correct! a) 15 − 7 = 8, b) 50 − 23 = 27, c) 61 − 34 = 27. Great use of inverse operations!

✗Some answers need another look. Remember: to solve an addition equation, subtract the same number from both sides.

Practice 3

Solve each subtraction equation. Write the value of the variable.

Remember: Subtraction equations use the inverse operation of subtraction, which is addition. Add the same number to both sides to isolate the variable.

a. m − 6 = 11 → m =

b. p − 15 = 28 → p =

c. k − 42 = 58 → k =

Sentence frame: "To solve ___ − ___ = ___, I add ___ to both sides and get ___ = ___."

✓All correct! a) 11 + 6 = 17, b) 28 + 15 = 43, c) 58 + 42 = 100. You used the inverse operation perfectly!

✗Some answers need another look. To solve a subtraction equation, add the same number to both sides.

Practice 4

Drag each word problem to the equation that represents it.

Key words: "more than," "added," "total" often mean addition (+). "Less than," "gave away," "fewer" often mean subtraction (−). The unknown quantity becomes your variable.

Ava saved $8 more and now has $20.

Leo spent $13 and has $7 left.

A shelf had books removed; 25 remain from 40.

x + 8 = 20

x − 13 = 7

40 − x = 25

Pick one problem and explain how you matched it:

Sentence frame: "The problem says ___, which means ___. So the equation is ___."

✓All matched correctly! "Saved more" = addition, "spent" = subtraction, "removed" = subtraction. The variable represents the unknown in each situation.

✗Some matches are off. Read each problem again. Look for key words like "more" (add) or "spent" / "removed" (subtract). Try again!

Practice 5

Jayla solves x − 18 = 34 and gets x = 52. Is her solution correct?

How to check a solution: Replace the variable with the answer and see if both sides are equal.
Try it: 52 − 18 = ?

Explain how you verified the answer:

Sentence frame: "I substituted ___ for x. ___ − 18 = ___. Since ___ equals ___, the solution is ___."

✓Correct! Substituting: 52 − 18 = 34 ✓. Both sides are equal, so x = 52 is the correct solution. Both A and D are valid reasoning, but A directly shows the check.

✗Substitute 52 for x: 52 − 18 = 34. Both sides match! Jayla is correct. The answer is A.

Challenge

Write your own word problem that can be modeled by an addition or subtraction equation. Then write the equation and solve it. Show that your solution is correct.

Think about it: Choose a real-life situation (money, sports, cooking, etc.). Decide on a variable for the unknown. Use an inverse operation to solve.
Example pattern: "I had some ___. After adding/removing ___, I had ___."

Your word problem:

Your equation:

Solve and check (show your work):

Sentence frame: "My word problem is about ___. The equation is ___. To solve, I use the inverse operation of ___ which is ___. The solution is ___ = ___. I can check by substituting: ___."

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