Lesson 9 — Activity 3: Multi-Step Equations
The last main type of question is a multi-step equation. This is where you might have to put variables and/or constants together before completing the other steps to solve the equation.
Answer the following two-step equation:
4b + 7 = 15
In the multi-step method, you will need to make use of the techniques you used in solving one-step and two-step equations.
Just as with solving one-step or two-step equations, the goal in solving an equation is to have only variables on one side of the equals sign and numbers on the other side of the equals sign.
For example, you might have the following equation:
y + 3 + y = 18
This looks similar to the equations you have done before, but this time there are two groups of variable y.
Follow these steps:
1. Put similar variables together as follows:
Take out the 2y and a y and combine them:
2y + y = 3y
Now the equation is 3y + 3 = 18
Now, solve it as two-step equation:
2. 3y + 3 – 3 = 18 – 3
3y = 15
3. 3y = 15
y = 5
Another example would be 21 + 4z – 1z + 3 = 27
Put your like terms together (in this case, combine all the z's and numbers on the left side of the equation):
4z – 1z + 21 + 3 = 27
z + 24 =27
Then solve as a two step equation:
3z + 24 = 27
3z + 24 –24 = 27 – 24
3z = 3
3z = 3
z = 1
Looking at equations with so many numbers and variables can be confusing! Remember that you need to put like terms together. This means that you need to combine all the variables and the numbers on one side of the equation before you begin trying to solve it. This simplifies the equation so that you can work with it more easily.