Two-Step Equations

3x + 4 = 19 has two things done to x: multiplied by 3, then 4 added.

Undo in reverse order

The 4 was added last, so subtract it first. Then divide by 3.

Why reverse

Putting on socks then shoes is undone by taking off shoes then socks. Same idea.

With brackets

2(x + 5) = 16 can be divided by 2 first, giving x + 5 = 8.

Undo in reverse order

To build 3x + 5 you multiply by 3, then add 5. To undo it, reverse the order: subtract 5 first, then divide by 3. Getting dressed and undressed follow the same principle — the last thing on is the first thing off.

A worked case

For 3x + 5 = 20: subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. Two steps, each applied to both sides, each written down.

Dividing first is not wrong, just harder

You could divide everything by 3 first, giving x + 5/3 = 20/3, then subtract. The answer is the same but the numbers are worse. Choosing the order that keeps the arithmetic clean is a real part of the skill.

Substitute into the original

3(5) + 5 = 20, so x = 5 is correct. Always check against the equation you were given, not one of your rearranged versions — an error made at step one will survive a check against step two.