Expressions and Equations
Linear equations with the unknown on both sides
Solve equations that have the unknown on both sides, and use them to answer word problems.
Until now every equation had its unknown on one side and its numbers on the other. Now the unknown turns up on both sides, and the first job is always the same: get all of it onto one side, and all the plain numbers onto the other.
The balance never tips
An equation is a balance. Whatever you do to one side you must do to the other — add the same thing, take away the same thing, multiply or divide by the same thing — and it stays balanced. That single rule is every step you will ever take.
Have a play
The scale is level, and there is a mystery box on each side. Move the weights about and find out what keeps it level and what tips it over.
Worked example
Solve 5x + 2 = 3x + 12.
Take 3x from both sides: 2x + 2 = 12.
Taking away the smaller number of x terms keeps the x positive, which is fewer sign mistakes than the other way round.
Try it together
Now let us solve 6x - 1 = 2x + 15 together.
Same three moves: clear the x from the smaller side, clear the number from the x side, then divide.
1.Take 2x from both sides. How many x are left on the left-hand side?
Have a go
Have a go on your own: solve 8x + 3 = 5x + 18. x = ?
Hint: Take 5x from both sides first.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.