Get Started

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
Back to Home
Want step-by-step help and more practice?
Join the Full Algebra Course