Linear Equations: Keep Both Sides Equal
Understand that an equation is a balance, that doing the same thing to both sides keeps it true, and that the goal is to isolate the unknown so the equation reads x equals a number.
Before you try
What if you took 2 away from only one side of an equation? Would it still be true?
Try it out
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What happened?
Move a control to see what changes and why.
The balance uses tidy numbers that keep both sides whole. Real equations often give fractions or decimals.
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Try these ideas
- Solve 3x + 2 = 11 in two steps and check the substitution at the end.
- Turn on the one-sided preview and watch the scale tip.
- Set the difficulty to hard and solve an equation with negatives.
Why it works
An equation says two things are equal, like a balance scale that is perfectly level. As long as you do exactly the same thing to both pans, adding, subtracting, multiplying or dividing by the same amount, the scale stays level and the equation stays true. Do something to one side alone and the balance tips: the statement you have written is simply false.
Solving means peeling away everything around the x until it stands alone. In this simulator the x boxes and unit weights sit on a beam, and a working list records each step you apply. Divide is only offered when every term divides exactly, so the numbers stay whole, and a preview toggle shows what would happen if you changed one side only.
Check your understanding
Question 1 of 4
Why must you do the same operation to both sides of an equation?
What is the next step to solve 3x = 12?
You solve 5x + 3 = 23 and get x = 4. How can you check it?
In 4x + 1 = 2x + 9, what is a sensible first move?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
For parents & teachers
- Act out an equation with coins on two plates and remove the same amount from each.
- Ask your child to invent an equation whose answer is their age.
- Discuss where equations appear in daily life, like working out change or scaling a recipe.