Algebra · Lesson 6

Two-Step Equations

Now two things are attached to the variable. We'll peel them off one at a time — and the order we undo them in is the reverse of the order of operations.

Part 01

Two Things in the Way

In a one-step equation, only one thing was attached to the variable. Now look at this:

2x + 3 = 11

The variable x has two things done to it: it's multiplied by 2, and then 3 is added. To get x alone, we have to undo both — but the order matters.

Part 02

Undo in Reverse Order

Think about getting dressed: you put on socks, then shoes. To undo it, you take off your shoes first, then your socks — the reverse order.

Equations work the same way. The last thing done to x was + 3, so we undo that first. Then we undo the × 2. That means: add/subtract first, then multiply/divide — the reverse of the order of operations.

1

Undo the + 3 first (subtract 3 from both sides)

2x + 3 − 3=11 − 3 2x=8
2

Undo the × 2 (divide both sides by 2)

2x2=82 x=4
3

Check it

2(4) + 3=8 + 3 =11
Part 03

Track the Steps

Your turn to guide the solve. For each step, choose the move that gets the variable closer to being alone. Watch the order!

Interactive · Two-Step Solver
Part 04

Why Subtract First?

You could divide first — but watch what happens to 2x + 3 = 11 each way:

Divide first 😖
2x + 32 = 112
x + 1½ = 5½
…messy fractions
Subtract first 😀
2x = 8
x = 4
clean whole numbers

Both can reach the right answer, but subtracting first keeps the numbers tidy. Undo addition and subtraction before multiplication and division, and you'll avoid the mess.

Your Turn!

Practice & Earn Your Score

Solve each two-step equation. Fill in the intermediate line after the first move, then the final value. Press Check — you earn a point when both blanks are right on the first try.

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Nice work!

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