An equation is a balance scale. Do the same thing to both pans and find the weight of the mystery bag. Play, solve missions, crack puzzles and beat the clock.
Start here. An equation is a balance scale. The = sign says the left pan and the right pan weigh the same. A bag with the letter x on it holds a mystery weight. Your job is to find out what x is.
The golden rule. Whatever you do to one pan, do the same to the other pan. Take 3 blocks off the left? Take 3 blocks off the right. Then the scale stays balanced. Do it to only one pan and the scale tips!
Get the bag alone. To find x, we want the bag by itself on one pan. If x + 5 = 12, take 5 blocks off both pans. The left pan is just the bag, and the right pan shows what the bag weighs: 7. We write x = 7.
Undo the move. Adding is undone by taking away. Taking away is undone by adding. A group of equal bags is undone by sharing into equal groups. Splitting a bag into parts is undone by making both sides bigger.
Two steps. For 2x + 3 = 11, first take 3 blocks off both pans to get 2x = 8. Then share both pans into 2 equal groups to get x = 4. Always clear the loose blocks first, then deal with the bags.
Bags on both pans. For 3x + 4 = x + 10, take 1 bag off both pans. Then you have 2x + 4 = 10. Now it is a two-step equation.
Check your answer. Put your answer in place of x on both sides. If both pans weigh the same, you are right. For 2x + 3 = 11 and x = 4: left is 2 × 4 + 3 = 11. Right is 11. They match!
An equation says that two things are equal, like a balance scale that is perfectly level. It always has an equals sign. Both sides must have the same value.
If you change only one side, the two sides are no longer equal, and the scale tips. Doing the same thing to both sides keeps the equation true while you get x alone.
x is a letter that stands for a number we do not know yet. In this game it is the weight of one bag. Every bag with an x weighs the same.
Put your answer in place of x and work out both sides. If the two sides are equal, your answer is right. This is called substituting.
Just starting: one-step equations such as x + 3 = 8 and 3x = 12. I know the basics: two-step equations and sharing a bag into groups. Challenge me: bags on both pans and word problems.
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