Solving linear equations
An equation is a balance. Whatever you do to one side you do to the other, and the unknown falls out.
Part of your national curriculum
- Algebra: Substitute numerical values into formulae and expressions, including scientific formulae
- Algebra: Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement
Lesson overview
What you'll learn in this lesson
Solve linear equations in one variable
Key learning points
- • Inverse operations
- • Unknowns on both sides
This lesson at a glance
- 30 minutes
- 9 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 9
Watch first
Solving linear equations
An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.
In a nutshell
Solve linear equations in one variable
Explore the idea
Part 2 of 9
Learn
Inverse operations
Undo in reverse order: remove additions first, then divide by the coefficient. 3x + 7 = 22 becomes 3x = 15, so x = 5.
Explore the idea
Part 3 of 9
Learn
Unknowns on both sides
Move the smaller x term across first to keep the coefficient positive, then finish as normal. Always check by substituting back.
Quick check
Part 4 of 9
Quick check
Solve 4x − 5 = 19
Quick check
Part 5 of 9
Quick check
Solve 2x + 3 = x + 10
Quick check
Part 6 of 9
Quick check
Checking a solution means…
Challenge round
Part 7 of 9
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Mastery quiz
Part 8 of 9
Marked quiz
End of lesson quiz: Solving linear equations
3 questions, marked with the reasoning shown. No timer.
1. Solve 4x − 5 = 19
2. Solve 2x + 3 = x + 10
3. Checking a solution means…
Lesson round-up
Part 9 of 9
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 9 · Watch & discover
How this is going
- Not looked at yet
Substitute numerical values into formulae and expressions, including scientific formulae
- Not looked at yet
Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement