Two-Step Equations
25 two-step equations on two pages, like 7x + 12 = 26 and 6x − 2 = 40. Every solution is a whole number from 2 to 12. It's for 7th and 8th graders who can solve one-step equations and are ready to chain two steps.
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Undo the steps in reverse order
To build 7x + 12 from x, you multiply by 7 and then add 12. Solving undoes that backwards: subtract 12 from both sides to get 7x = 14, then divide by 7 to get x = 2.
Dividing first is allowed, but every term has to be divided, which gives x + 12/7 = 26/7. Students often divide the 7x and the 26 and forget the 12. Subtracting the constant first avoids both the fractions and that mistake.
With a minus sign, the first step is adding: 6x − 2 = 40 becomes 6x = 42, so x = 7. Have students check every answer by putting it back in the original equation.
Frequently Asked Questions
Why do you subtract before dividing?
Solving undoes the equation in the reverse of the order it was built. The multiplication happened first, so it gets undone last. The other order works too, but it brings fractions into the middle steps.
How do I check a two-step equation?
Put the value back in for x. For 3x + 8 = 20, x = 4 gives 3 × 4 + 8 = 20, so the answer checks out.
What grade learns two-step equations?
7th grade, where students solve equations like px + q = r. In 8th grade they build on it with variables on both sides.