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
- 12 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 12
Visual introductionPicture this
Solving linear equations
An equation is a balance. Whatever you do to one side you do to the other, and the unknown falls out.
In a nutshell
Solve linear equations in one variable
Explore the idea
Part 2 of 12
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 12
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.
Reset break
Part 4 of 12
Pause
That's sitting 1 of 3 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.
Quick check
Part 5 of 12
Quick check
Part 6 of 12
Quick check
Part 7 of 12
Reset break
Part 8 of 12
Pause
That's sitting 2 of 3 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 9 of 12
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 10 of 12
Game · Recall cards
If x=4, find 3x+2.
Card 1 of 4
Mastery quiz
Part 11 of 12
Marked quiz
End of lesson quiz: Solving linear equations
4 questions, marked with the reasoning shown. No timer.
1. If x=4, find 3x+2.
2. Using v=d/t, find v when d=150 m and t=12 s.
3. If a=−3, what is a²?
4. Solve 4x − 5 = 19
Lesson round-up
Part 12 of 12
Lesson round-up
Ready when you are
Quiz score
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Points this lesson
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Best run
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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 12 · 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