Why do I always get stuck on the last step of algebra puzzles?

I really enjoy algebra puzzles, but I keep running into the same issue — I can work through the setup fine, but when I reach the final step to isolate the variable, I always second-guess myself.

For example, if I end up with something like 3x – 8 = 10, I freeze and forget which way to move the numbers. I know it’s basic, but it’s becoming frustrating.

Does anyone have a simple trick or mental shortcut that helps with this?

3 Responses

  1. A simple way to avoid freezing is to think “undo in reverse.” Ask: what was done to x, and in what order? In 3x − 8 = 10, x was first multiplied by 3, then 8 was subtracted. Undo the last thing first: add 8 to both sides to get 3x = 18, then divide both sides by 3 to get x = 6. Quick check: 3·6 − 8 = 18 − 8 = 10, so it works.

    A small habit that helps: say the steps aloud as “opposite, both sides, reverse order.” Write the operation you’re undoing next to the line (e.g., +8, then ÷3) so you don’t second-guess the direction. Avoid the idea of “moving numbers across and changing signs”; just do the inverse operation to both sides and keep the equation balanced.

  2. I totally get that freeze-think of an equation like a balance scale and x as someone who got dressed in steps: first x was multiplied by 3, then 8 was taken away, and the result equals 10; to “undress” x, you undo the actions in reverse, like taking off shoes before socks. So your mantra is: undo last thing first, on both sides to keep balance. In 3x − 8 = 10, the last thing done to x was “−8,” so you add 8 to both sides: 3x = 18. Now undo the earlier “×3” by dividing both sides by 3: x = 6. Quick confidence boost: plug it back in-3·6 − 8 = 18 − 8 = 10-works! This avoids the confusing “move it across and change the sign” idea and replaces it with a clear story: what happened to x, and how do I reverse it? Does the “undo in reverse order” picture click for you, or should we try another example you’ve gotten stuck on?

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