Time to put the balance scale to work. An equation says two sides are equal — and we can uncover the mystery number by doing the same thing to both sides until the variable stands alone.
An equation is a sentence with an equals sign, like x + 3 = 7. Solving it means finding the one value of x that makes the sentence true.
Here, x has to be 4, because 4 + 3 = 7. The goal every time is the same: get the variable all by itself on one side. We call that isolating the variable.
The variable doesn't have to be x. It could be y, n, b, or any letter at all — it's just a placeholder for the mystery number. Whatever letter you see, you solve it the exact same way. (You'll spot all kinds of letters in the practice below.)
Think of the equals sign as the middle of a balance scale. The two sides weigh the same. So if you change one side, you must do the exact same thing to the other side — otherwise it tips and is no longer true.
To get the variable alone, you undo whatever is attached to it, using the inverse (opposite) operation:
Dividing is often written with a fraction bar instead of a ÷ sign. So x ÷ 6 and x6 mean exactly the same thing — "x divided by 6." The number on top is the numerator and the number on the bottom is the denominator. You'll see division written this way on the scale and in the practice below, and to undo it you do the inverse: multiply.
Here, 3 is added to the variable.
The inverse of + 3 is − 3, so subtract 3 from each side:
The + 3 and the − 3 cancel out, leaving:
Your turn to balance. The scale below shows an equation. Choose the move that undoes what's attached to the variable — remember to think about the inverse operation. The same move happens to both sides automatically.
Every one-step equation is one of these four. The move to solve it is always the inverse of what you see:
Put your solution back into the original equation. If both sides come out equal, you've got it right. For x + 3 = 7 with x = 4: 4 + 3 = 7. ✓
Solve each equation for its variable — watch out, the letter changes from problem to problem! Type the value and press Check. You earn a point for each one you get on the first try, and the full worked solution appears once you check.