Throughout this week in Math 9 we have been working on linear equations and the rules that go along with them. For this assignment, I will explain how to do linear equations with variables and constants on both sides.
To do linear equations, you need to remember a few key steps and rules:
1. You want to move the variables to 1 side of the equation, and the constants to the other. You can do this for which ever side you find easier (ex moving the smaller variable so you don’t have to deal with a negative variable)
2. When moving anything across the = sign, turn it into the inverse of itself (negatives to positive, positive to negative).
3. Add everything on each individual side together.
4. Divide the constant (on the other side of the equals sign) by the coefficient of the variable (if necessary). This will result in the answer for 1 of the variable (ex. 1y). However, if the coefficient was negative, it will result in the answer for -1y, in which case you need to turn it into the inverse of itself.
5. Double check your answer by going to the original question, and plugging the answer in, replacing the variable. See if it checks out.
Example 1:
2x = x + 1
2x – x = 1 (Moving x across the equals sign makes it negative)
x = 1 (Add everything on each individual side together)
Verifying example 1:
2x = x + 1
2*1 = 1 + 1
2 = 1 + 1
2 = 2
Example 2:
6x + 10 – 4x = 12x – 20
10 + 20 = 10x (Moving -20 across the equals sign made it positive, moving 6x made it negative, moving -4x made it positive. All the constants are now on one side, and all the variables are on the other)
30 = 10x (Add everything on each individual side together)
30/10 = 3 (Divide the constant by the coefficient, the coefficient is positive so we now have the result for positive 1x)
x = 3
Verifying example 2:
6x + 10 – 4x = 12x – 20
6*3 + 10 – 4*3 = 12*3 – 20
18 + 10 – 12 = 36 – 20
16 = 16