In $3x + 5 = 20$, two things happened to $x$: it was multiplied by 3, and then 5 was added. You know how to undo each one from one-step equations. The question is the order.
Key idea
Undo the steps in reverse order: first undo the adding or subtracting, then undo the multiplying or dividing. Do each step to the whole of both sides.
Why it works
Getting dressed, you put on socks, then shoes. Undressing, you take off the shoes first. Here $x$ was multiplied first and the 5 was added last, so the 5 comes off first. You could divide first, but then every term must be divided, $x + \frac{5}{3} = \frac{20}{3}$, which is correct but messier.
Worked examples
Worked example: Positive numbers
Solve $3x + 5 = 20$.
- Subtract 5 from both sides: $3x = 15$.
- Divide both sides by 3: $x = 5$.
- Check: $3(5) + 5 = 20$ ✓.
Answer: $x = 5$
Worked example: Negative numbers
Solve $-4x - 7 = 13$.
- Add 7 to both sides: $-4x = 20$.
- Divide by $-4$: $x = -5$.
- Check: $-4(-5) - 7 = 20 - 7 = 13$ ✓.
Answer: $x = -5$
Worked example: Dividing instead of multiplying
Solve $\frac{x}{5} + 3 = -1$.
- Subtract 3: $\frac{x}{5} = -4$.
- Multiply by 5: $x = -20$.
- Check: $-20 \div 5 + 3 = -4 + 3 = -1$ ✓.
Answer: $x = -20$
Common mistake
Dividing only part of a side: from $3x + 5 = 20$ writing $x + 5 = \frac{20}{3}$. If you divide, you must divide every term. Safer: undo the $+5$ first. Always check by substituting your answer into the original equation.