One-Step Equations

Start with x + 7 = 12. The 7 is stuck to x by adding, so subtract 7 — from both sides. Writing the middle line out in full is worth doing while you are learning: it shows a marker that you did the same thing to both sides, and it stops you dropping a step. The left becomes x, the right becomes 5, so x = 5. Check by substituting: 5 + 7 is 12, correct.

Now y − 4 = 9. Here the 4 is stuck on by subtracting, so you undo it by adding 4 to both sides, giving y = 13. This is the one that trips people up, because the equation has a minus sign in it and subtracting feels like the natural move. Resist that. Look at what is being done to y — it is being reduced by 4 — so to undo it you must add. The check settles any doubt: 13 minus 4 really is 9.

5x = 35 looks different because there is no visible operation sign — but 5x means 5 times x, so the multiplication is there, just hidden. Nothing is being added, so subtracting 5 would be wrong and would give 30. Divide instead: both sides by 5, giving x = 7. It helps to read 5x aloud as five lots of x, because then the question becomes obvious — if five lots come to 35, one lot is 7.

The last one is division: x divided by 3 equals 6. Undo it by multiplying both sides by 3, giving x = 18. You will more often see this written as a fraction, x over 3 equals 6, and that is exactly the same equation — a fraction bar just means divide. So whenever you see the pronumeral sitting on top of a fraction, multiply both sides by whatever is underneath.

Look at these four together. They all use 8 and 20, and the answers are 12, 28, 2.5 and 160 — wildly different. What separates them is only what is being done to x. So make reading the equation a separate step from solving it: look at x, name what has been done to it, then do the opposite to both sides. Students who rush straight to calculating are the ones who subtract when they should have divided.