Two-step equations: how to help your child practice

What is a two-step equation?

A two-step equation is an equation where the unknown has two things done to it. In 2x + 5 = 17, the number x is multiplied by 2 and then has 5 added. To find x, you undo those two things, in reverse order.

Think of it like getting dressed: socks first, then shoes. To get undressed, shoes come off first, then socks. The equation did "times 2, then plus 5," so you undo "plus 5" first, then "times 2."

The golden rule is balance: whatever you do to one side of the equal sign, you do to the other, so both sides stay equal.

In most US schools, 7th graders solve equations like 3x + 4 = 19 and word problems that lead to them, and 8th graders solve multi-step equations, including ones with the variable on both sides. The 7th grade guide covers what else comes up that year, and the 8th grade guide shows where algebra goes next.

How do you solve a two-step equation, step by step?

Use the same routine every time. Here is 3x − 4 = 11:

1. Undo adding or subtracting. The 4 is subtracted, so add 4 to both sides: 3x − 4 + 4 = 11 + 4, which gives 3x = 15.
2. Undo multiplying or dividing. x is multiplied by 3, so divide both sides by 3: x = 15 ÷ 3 = 5.
3. Check by substituting. Put 5 back in: 3 × 5 − 4 = 15 − 4 = 11. It matches, so x = 5.

The same steps work when x is divided. For x/3 + 2 = 9, subtract 2 from both sides (x/3 = 7), then multiply both sides by 3 (x = 21).

Watch the signs when the number in front of x is negative. In −3x + 4 = 19, subtract 4 to get −3x = 15, then divide by −3 to get x = −5. Check: −3 × −5 + 4 = 15 + 4 = 19.

What two-step equations mistakes do kids make most?

Dividing before subtracting

For 2x + 5 = 17, a child divides only the 17 by 2 and gets x + 5 = 8.5, so x = 3.5. Checking shows the problem: 2 × 3.5 + 5 = 12, not 17. Undo the + 5 first (2x = 12), then divide (x = 6).

Using the same operation instead of the opposite

For 4x − 7 = 21, a child subtracts 7 from both sides and gets 4x = 14, so x = 3.5. To undo subtracting 7, add 7: 4x = 28, so x = 7. Have your child say what was done to x, then name the opposite.

Dropping a negative sign

For −3x + 4 = 19, a child gets −3x = 15 and then writes x = 5. Dividing by −3 gives x = −5. Substituting catches it: −3 × 5 + 4 = −11, not 19.

How can you practice two-step equations at home in 10 minutes?

A few equations solved carefully and checked beat a long page solved quickly.

• Minutes 1–3: think of a number. Say, "I'm thinking of a number. I doubled it and added 3, and got 17. What's my number?" (7.) Then have your child write it as 2x + 3 = 17 and solve it on paper.
• Minutes 4–8: five mixed problems. One with adding (5x + 2 = 27), one with subtracting (3x − 8 = 13), one with dividing (x/2 + 6 = 10), one with a negative (−2x + 5 = 11), and one word problem. 8th graders can swap one for an equation with x on both sides (5x + 3 = 2x + 18).
• Minutes 9–10: check every answer. Your child substitutes each answer back into its equation. If both sides don't match, find the step that went wrong.

Use new numbers each night so your child practices the moves, not the answers.

How can Easy Twin help with two-step equations?

Scan your child's algebra worksheet and Easy Twin makes a twin with the same kinds of questions and new numbers, so practice stays on exactly what the class is learning. Every question comes with two hints and worked steps, and your child can play the twin as a quest or you can print it with an answer key.

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