Two-step equations

Two operations, two undos

In $2x + 3 = 11$, two things happened to $x$: it was multiplied by 2, then 3 was added. To get $x$ alone, you'll need to undo both. But which first?

Try it. Can you split into $2$ groups right away?

Splitting first doesn't work: the $3$ loose weights on the left can't be shared evenly between $2$ groups. Clear the loose weights first, and the split comes out clean.

Undo in reverse order

Think of getting dressed: socks go on before shoes, so shoes come off first. Undo the operations in reverse order: the last thing done is the first thing undone. For $2x + 3$, multiplying happened first and adding happened last, so subtract first and divide second.

One more. Before you start, predict which move comes first and which comes second.

With negatives

The same two steps work when numbers are negative. Watch the signs.

When $x$ is divided

If $x$ is divided by a number, clear the constant first, then multiply.

The constant can come first

$7 + 2x = 19$ is the same equation as $2x + 7 = 19$, only written in a different order. Subtract $7$, then divide by $2$, and $x = 6$.

Key ideas

• Undo operations in reverse order: addition or subtraction first, then multiplication or division.
• Every step is done to both sides, so the equation stays balanced.
• Check your answer by substituting it into the original equation.