Equation Balance
Solve equations on a balance scale: do the same thing to both sides until x stands alone. Step-by-step algebra for grades 6 to 8.
How to use it
Each x box hides the same unknown weight, and each round weight is 1. The scale is balanced, so both sides weigh the same. Choose an amount, then a move. Every move happens to both sides, so the scale stays level. Keep going until one side holds a single x box and the other holds only round weights: that is the answer.
Start with One step, then Two steps, then x on both sides. In Type your own, enter an equation like 4x + 3 = 2x + 11 using whole numbers and plus signs.
Why "do the same to both sides" works
An equation says two amounts are equal, just like a balanced scale. If you take the same weight off both pans, or add the same weight to both, it stays balanced. If you split both pans into the same number of equal groups, one group from each side still balances. These moves change how the equation looks, not its solution.
Solving is choosing moves that get x by itself. A good order is: first take away x boxes so x is on one side only, then take away the loose weights on that side, then divide to find one x. The tool refuses moves a real scale couldn't do (taking away weights that aren't there) and divisions that would cut a box or a weight into pieces. Fractions are fine in algebra, but this tool keeps everything whole so the picture stays honest.
- Ask: "What could you do to both sides that gets rid of the 5 on the left?"
- After solving, put the answer back into the original equation to check it.
- Why is "add 3 to both sides" allowed but not helpful here?
Free to use, no account needed. It runs in your browser: nothing you type, and no sound from your microphone, is sent to Fieldbook.
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