Word Problems
Turn real-world situations into equations.
What You will learn:
-
Translate words into math -
Set up equations -
Solve step-by-step -
Check answers
Lesson 1: Translate Words –
keep it simple
“A number plus 7 is 15”
↓
x + 7 = 15
Solve:
1
Subtract 7 from both sides
x + 7 − 7 = 15 − 7
2
x = 8
✔
Check:
8 + 7 = 15
✔
Lesson 2: Set Up the Equation –
one step up
“Twice a number plus 5 is 13”
↓
2x + 5 = 13
Solve:
1
Subtract 5 from both sides
2x + 5 − 5 = 13 − 5
2
2x = 8
3
Divide both sides by 2
2x ÷ 2 = 8 ÷ 2
4
x = 4
✔
Check:
2(4) + 5 = 13
✔
Lesson 3: Solve It –
introduce a real context
“Three times a number minus 4 is 11”
↓
3x − 4 = 11
Solve:
1
Add 4 to both sides
3x − 4 + 4 = 11 + 4
2
3x = 15
3
Divide both sides by 3
3x ÷ 3 = 15 ÷ 3
4
x = 5
✔
Check:
3(5) − 4 = 11
✔
Problem: A phone plan charges a $25 monthly fee plus $0.10 per text message. Last month, Maya’s bill was $43. How many text messages did she send?
Step-by-Step Solution:
1
Set up the equation (Let x = texts)
25 + 0.10x = 43
2
Subtract 25 from both sides
0.10x = 43 − 25
3
Result after subtraction
0.10x = 18
4
Divide both sides by 0.10
x = 18 ÷ 0.10
5
x = 180
✔
Final Answer:
Maya sent 180 text messages.
Practice Problems
Easy
- A number minus 9 is 14
- x − 9 = 14
Medium
- Three times a number plus 4 is 19
- 3x + 4 = 19
Challenge
- A real-world scenario
- Maya earns $12 per hour. After working some hours this week, she has $108. How many hours did she work?
- Solve: Add 9 to both sides
- x − 9 + 9 = 14 + 9 x = 23
- Solve: Subtract 4 from both sides
- ↓
- 3x + 4 − 4 = 19 − 4 3x = 15
- ↓
- Divide both sides by 3
- ↓
- 3x ÷ 3 = 15 ÷ 3 x = 5
- 12x = 108
- Divide both sides by 12
- 12x ÷ 12 = 108 ÷ 12 x = 9
Practice Problems
Common Mistakes to Avoid
-
Forgetting to do the same operation to both sides -
Skipping steps or moving too fast -
Not checking your answer
Quick Recap:
Answer Key:
Easy:
23 − 9 = 14
Medium:
3(5) + 4 = 19
Challenge:
12(9) = 108
Next:
Factoring
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