Chapter 5: Solving linear equations
An equation is a balance: every operation must preserve equality on both sides.
Part of your national curriculum
- 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
Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement
Key learning points
- • Inverse operations
- • Unknowns on both sides
- • Check
This lesson at a glance
- 32 minutes
- 16 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 16
Visual introductionPicture this
Chapter 5: Solving linear equations
An equation is a balance: every operation must preserve equality on both sides.
In a nutshell
Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement
Learning cycle
Part 2 of 16
Learning cycle 1 of 2
Part 1 · Inverse operations
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 16
Learn
Inverse operations
Solve 4x − 7 = 21 by adding 7 to both sides, then dividing both sides by 4. This gives x = 7.
Reset break
Part 4 of 16
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 16
Learn
Unknowns on both sides
For 5x + 2 = 2x + 20, subtract 2x from both sides, then subtract 2: 3x = 18, so x = 6.
Quick check
Part 6 of 16
Quick check
Part 7 of 16
Reset break
Part 8 of 16
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 16
Learning cycle 2 of 2
Part 2 · Check
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 16
Learn
Check
Substitute the solution into the original equation. Both sides must produce the same number; if not, revisit each transformation.
Quick check
Part 11 of 16
Reset break
Part 12 of 16
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 16
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
Challenge round
Part 14 of 16
Game · Recall cards
Solve 4x−7=21.
Card 1 of 4
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Chapter 5: Solving linear equations
4 questions, marked with the reasoning shown. No timer.
1. Solve 4x−7=21.
2. Solve 5x+2=2x+20.
3. Why substitute the solution back?
4. Solve 4x − 5 = 19
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
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Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement