Solving a Multi-Step Algebraic Equation
A multi step equation is an equation where more than 2 mathematical steps are required to solve the
equation
For example: 4x+9=2x-6 To solve this you need to move the variables (the x’s ) together and then get the variable
by itself on one side of the equation
4x+9=2x-6
First you move all the variables to one side of the equation by subtracting 2x from both sides
2x+9=-6
Then you get rid of the other number in the side of the variable by subtracting 9 from both sides
2x=-15
Now you get rid of the coefficient by dividing both sides by 2
x= - 152
Now you know the value of the variable meaning that you have solved a multi step equation.
As you can see in the example 3 steps were included to solve the equation. Now here is how to solve a real word
problem:
To be able to solve the mathematical problem we must first write it as an algebraic equation. We can make R the
regular amount of cup cakes (the variable.) So the equation will look like this:
r
2
+ 5r=6r -10
The first step of solving this equation can either be to move all the variables to one side or get rid of the
coefficients. I am going to start by removing the coefficients. To do this I will first multiply both sides of the
equation by 2. The equation will now look like this.
r+10r= 12r -20
Then I will bring over all variables to one side of the equation by subtracting 12r from both sides of the equation.
The equation will now look like this
-1r= -20
Then I will get rid of the remaining coefficient by dividing by -1 on both sides of the equation. This is what the
equation will look like now and since it was the final step this is your solution.
r=20
To check if your solution is correct simply take the original equation and replace all variables with your answer. If
the equation still makes senses than your solution was correct if not however you should try find the solution
again. This is what the equation look like when checking:
20
2 + 5(20)=6(20) -10
The first half of the equation is equal to 110 (10+100). The second half is also equal to 110 (120 - 10) This proves that
your solution makes sense and is correct
.