Variables on both sides, step by step
5x + 3 = 2x + 18 is the first equation that needs a decision before it needs arithmetic.
10x + 13 = 12x + 3
- This one has x on BOTH sides, so nothing can be undone yet — subtracting 13 would still leave an x on the right. Collect the x terms first.
- Take 10x off BOTH sides. That clears x from the left, leaving 13 = 2x + 3. An equals sign does not care which side is which, so write it as 2x + 3 = 13. That is an equation you have already met.
- Two things were done to x: multiplied by 2, then 3 added. Undo them in the REVERSE order — whatever happened last comes off first.
- The 3 went on last, so it comes off first — and off BOTH sides, or the two halves stop being equal. 13 − 3 = 10.
- That leaves 2x, which means 2 lots of x. Divide both sides by 2: 10 ÷ 2 = 5.
- Check by putting it back into the ORIGINAL, both sides: 10(5) + 13 = 63, and 12(5) + 3 = 63 — both 63, so x = 5.
How it works.
- 01
This one has x on BOTH sides, so nothing can be undone yet — subtracting 13 would still leave an x on the right. Collect the x terms first.
- 02
Take 10x off BOTH sides. That clears x from the left, leaving 13 = 2x + 3. An equals sign does not care which side is which, so write it as 2x + 3 = 13. That is an equation you have already met.
- 03
Two things were done to x: multiplied by 2, then 3 added. Undo them in the REVERSE order — whatever happened last comes off first.
- 04
The 3 went on last, so it comes off first — and off BOTH sides, or the two halves stop being equal. 13 − 3 = 10.
- 05
That leaves 2x, which means 2 lots of x. Divide both sides by 2: 10 ÷ 2 = 5.
- 06
Check by putting it back into the ORIGINAL, both sides: 10(5) + 13 = 63, and 12(5) + 3 = 63 — both 63, so x = 5.