Two step equations take two inverse operations to solve. Here is the order to use, nine worked examples, and the mistakes that cost the most points.
What are two step equations?
Two step equations are equations you can solve with exactly two inverse operations. A typical one looks like 3x + 5 = 20: the x is multiplied by 3, and then 5 is added.
To get x by itself, you undo those two things in reverse order. That idea is all there is to it, and every example below follows it. If you are still getting comfortable with one step equations, the general strategy in our guide to solving linear equations step by step covers the groundwork.
How do you solve two step equations?
To solve a two step equation, first add or subtract to move the constant term away from the variable, then multiply or divide to clear the coefficient. Whatever you do to one side, you do to the other.
Think of it like taking off shoes and socks. You put the socks on first, so they come off last. In 3x + 5, multiplication by 3 happened first and the + 5 happened last, so the + 5 is the first thing you undo.
- Find the constant term on the same side as the variable.
- Add or subtract that number on both sides so the variable term stands alone.
- Divide both sides by the coefficient (or multiply by its reciprocal if it is a fraction).
- Substitute your answer into the original equation to check it.
What do two step equations examples look like with whole numbers?
Here are two more with positive whole numbers. Both use the same order: undo the constant, then undo the coefficient.
In 2x − 7 = 11, the 7 is subtracted, so you add 7 to both sides. That leaves 2x = 18, and dividing by 2 gives x = 9.
How do you solve two step equations with negative numbers?
Negative numbers don’t change the steps. You still undo the constant first, then divide by the coefficient, sign included.
Take −4x + 9 = 1. Subtract 9 from both sides to get −4x = −8. Now divide by −4, and since a negative divided by a negative is positive, x = 2.
How do you solve two step equations with fractions?
When the coefficient is a fraction, the second step is multiplying by its reciprocal instead of dividing. The first step stays the same.
For x/3 + 4 = 10, subtract 4 to get x/3 = 6. The x is divided by 3, so multiply both sides by 3: x = 18.
What if the whole side is divided, like (x + 4)/5 = 3?
When the entire expression is divided, the order flips: multiply first, then subtract. The division bar acts like parentheses, so the + 4 happened inside, before the division.
Multiply both sides of (x + 4)/5 = 3 by 5 to get x + 4 = 15. Subtract 4 and you have x = 11.
What are the most common mistakes?
The most common mistake is dividing first and only dividing part of the side. In 3x + 5 = 20, dividing by 3 means every term gets divided, which gives x + 5/3 = 20/3. That is legal but messy, and students often forget to divide the 5.
Here are the slips that show up most often on homework:
Why do you undo addition before multiplication?
Because solving runs the order of operations backward. To build 3x + 5 from x, you multiply by 3 first and add 5 second, so to take it apart you remove the 5 first and the 3 second.
You can divide first if you want, but then every term has to be divided. 3x + 5 = 20 becomes x + 5/3 = 20/3, and subtracting 5/3 still lands on x = 5. Same answer, more fractions. The usual order keeps the numbers whole for as long as possible.
How do you solve 2 step equations from word problems?
To solve 2 step equations from a word problem, write the equation first, then solve it the same way. Look for a starting amount (the constant) and a rate or repeated amount (the coefficient).
Say a gym charges a $5 sign-up fee plus $3 per class, and you spent $20. That is 3x + 5 = 20, the first equation in this article, so you took 5 classes.
How can you check your work quickly?
Substitute your answer into the original equation. If both sides match, the answer is right.
For a second opinion, type the equation into the two-step equation calculator. It shows each inverse operation on its own line, so you can compare it with your work and spot exactly where the two differ. Equations with x on both sides, like 6x + 4 = 2x − 8 (which gives x = −3), take one extra step and fit better in the linear equation solver.
Frequently asked questions
What is a two step equation?
A two step equation is an equation that takes two inverse operations to solve, such as 3x + 5 = 20. You subtract 5 and then divide by 3 to get x = 5.
Do you add or divide first in a two step equation?
Usually you add or subtract first, then multiply or divide. The exception is when the whole side is divided, as in (x + 4)/5 = 3, where you multiply by 5 first.
How do you solve a two step equation with a fraction?
Move the constant first, then multiply both sides by the reciprocal of the fraction. For (2/3)x + 1 = 9, subtract 1 to get (2/3)x = 8, then multiply by 3/2 to get x = 12.
Can the answer to a two step equation be negative?
Yes. In 5 − 2x = 17, subtracting 5 gives −2x = 12, and dividing by −2 gives x = −6. A negative answer is just as valid as a positive one.
How do I know my answer is right?
Put it back into the original equation and simplify both sides. If they are equal, the answer is correct. If not, recheck the sign on each step.
What is the difference between one step and two step equations?
A one step equation like 3x = 15 needs a single inverse operation. A two step equation like 3x + 5 = 20 needs two, and you undo the addition or subtraction before the multiplication or division.