Expressions and Equations
Solving equations
Solve a linear equation in one variable by keeping both sides balanced.
An equation is a pair of scales that balance. The equals sign says the left-hand side weighs exactly the same as the right-hand side, and solving the equation means working out what the letter must be for that to be true.
The golden rule
Whatever you do to one side, do to the other. Take 3 off the left and you must take 3 off the right, or the scales tip and the equation stops being true.
Have a play
Two mystery boxes and some weights, and the beam is level. See how much you can take away without it moving.
Worked example
Solve 2x + 3 = 11.
The x has a 3 stuck to it, so take 3 off both sides. That gives 2x = 8.
Peel away whatever is furthest from the x first — the adding, before the multiplying.
Try it together
Your turn: solve 5x - 7 = 18.
Same two moves as before — undo the subtracting, then undo the multiplying.
1.Add 7 to both sides. The left becomes 5x. What does the right-hand side become?
When letters appear on both sides
Gather them first. For 2x + 1 = x + 9, take x off both sides to get x + 1 = 9, and now it is an ordinary one-step problem.
Have a go
Have a go on your own: 3x + 2 = 20. What is x?
Hint: Take 2 off both sides, then divide by 3.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.