01 · DISCOVER
Solving Equations and Inequalities: before you begin
Build your understanding of solving equations and inequalities through examples and practice. Explain each step and check whether your answer makes sense. For related lessons, return to the math pathway collection. When your teacher allows it, use the Desmos graphing calculator to check coordinates, equations, or calculations.
Enter your name and school email to save your learning. You’ll explore solving equations and inequalities and then practice 12 questions with feedback.
Success criteria
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we use solving equations & inequalities to solve problems?
02 · LEARN & EXPLORE
Where this matters
Equations and inequalities describe unknown quantities and limits in budgets, planning, and measurement.
03 · LEARN & EXPLORE
Understand the mathematics
Solve 3x + 5 = 20: subtract 5 from both sides to get 3x = 15, then divide by 3 to obtain x = 5. For inequalities, reverse the sign only when multiplying or dividing by a negative number.
Trace each operation and verify the result by checking the original problem.
Subtract five from both sides of 3x + 5 = 20, then divide by three.
04 · LEARN & EXPLORE
Model the first situation
Solve x + 8 = 21 by subtracting 8 from both sides. The solution is x = 13.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Equations and inequalities describe unknown quantities and limits in budgets, planning, and measurement.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
Solve 3x − 5 = 16: add 5 to both sides, giving 3x = 21, and divide by 3 to get x = 7.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
Solve −2x < 10: divide by −2 and reverse the inequality sign, giving x > −5.
Strategy reminder: Maintain balance by applying the same operation to both sides. Flip the inequality only when multiplying or dividing by a negative.
08 · LEARN & EXPLORE
Connect the idea
Equations describe exact equality; inequalities describe a range of possible values. Use inverse operations while preserving equality or inequality.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
Solve 2x – 7 = 9.
Choose the best answer, then study the feedback.
Add 7, then divide by 2.
INDEPENDENT PRACTICE · 2 OF 12
Which values satisfy x + 4 > 10?
Work independently and check that your answer makes sense.
Subtract 4 from both sides.
INDEPENDENT PRACTICE · 3 OF 12
x+7=12. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 4 OF 12
3x=21. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 5 OF 12
2x+5=17. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 6 OF 12
x-9=-2. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 7 OF 12
4x-3=13. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 8 OF 12
x/3=8. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 9 OF 12
x+4>10 means
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 10 OF 12
-2x<10 means
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 11 OF 12
5x+2=27. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 12 OF 12
3(x-2)=12. Find x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.