Multi-step equations

Multi-step equations are all equations that require you to perform more than two steps (or operations) in order to solve them. They can be simple or really hard to do, since there are no limitations on the number of steps you have to perform to get to a solution. But one thing is certain – they will require all the knowledge you gained by solving one-step equations and two-step equations. Because this is a bit more complicated, we will show you how to solve multi-step equations on two examples.

The first example is a fairly simple multi-step equation with integers that has a variable on both sides of the equation.

n + 2 = -4 + 2n

The first thing we have to do here is to get all the variables on one side and all the numbers on the other.  It does not matter on which ones you put on the right side of the equation and which ones on the left – you will still get the same result in the end. But in this case, we will save ourselves a bit of effort if we put the variables on the right side.

2 + 4 = 2n – n

Now we perform the calculations and get…

6 = n

This was easy, was it not? By making a smart choice in the beginning, we made the equation easier to solve. Otherwise, we would have to perform an additional operation. Like this:

n + 2 = -4 + 2n

n – 2n = -4 – 2

-n = -6 |*(-1)

n = 6

It does not seem like a big deal now, but thinking and a bit of planning instead of automatic solving can help you a lot when dealing with some multi-step equations.

Now, let us try to solve a more complicated equation. An equation like this one:

6n – 3(-3n + 2) = -24 + 6n

This equation requires us to perform a distribution, so we will do that first. That means we have to multiply each element between the brackets with the number in front of the brackets, or in this case “-3”.

6n – 3*(-3n) + (-3)*2 = -24 + 6n

When we clean that up a bit, we get:

6n + 9n – 6 = -24 + 6n

Now we will move the variables to the left side and the numbers to the right side.

6n + 9n – 6n = -24 + 6

When we perform the additions and subtractions, we get:

9n = -18

All that is left to do now is to divide the whole equation by 9 and…

9n = -18 |:(9)

n = 2

…we found the solution.

multi step equations

If you want to practice solving multi-step equations some more, use the free worksheets below.

Multi-step equations  exams for teachers

Exam Name File Size Downloads Upload date
Integers
Multi-step equations – Integers – very easy 527.8 kB 5916 October 13, 2012
Multi-step equations – Integers – easy 526 kB 6433 October 13, 2012
Multi-step equations – Integers – medium 530.7 kB 12962 October 13, 2012
Multi-step equations – Integers – hard 535.4 kB 8783 October 13, 2012
Multi-step equations – Integers – very hard 533 kB 7274 October 13, 2012
Decimals
Multi-step equations – Decimals – very easy 542.5 kB 1313 October 13, 2012
Multi-step equations – Decimals – easy 541.7 kB 1446 October 13, 2012
Multi-step equations – Decimals – medium 541.8 kB 2012 October 13, 2012
Multi-step equations – Decimals – hard 551.4 kB 1199 October 13, 2012
Multi-step equations – Decimals – very hard 579.6 kB 1112 October 13, 2012
Fractions
Multi-step equations – Fractions – very easy 554.5 kB 4627 October 13, 2012
Multi-step equations – Fractions – easy 558.1 kB 4853 October 13, 2012
Multi-step equations – Fractions – medium 556.5 kB 5642 October 13, 2012
Multi-step equations – Fractions – hard 566 kB 2523 October 13, 2012
Multi-step equations – Fractions – very hard 596.5 kB 2241 October 13, 2012


Multi-step equations worksheets for students

Worksheet Name File Size Downloads Upload date
Multi-step equations – Integers 222.1 kB 7724 October 14, 2012
Multi-step equations – Decimals 261.5 kB 1731 October 14, 2012
Multi-step equations – Fractions 697.3 kB 4020 October 14, 2012


Multi-step equations knowledge test