Unit 2.3 Solving Linear Equations
Solving Linear Equations
A linear equation is an algebraic expression that is set equal to a value.
5x + 4 = 1
To solve a linear equation, the goal is to isolate the variable so that it equals a constant. This can be done by adding, subtracting, multiplying and dividing. The variable should be the only thing on one side of the equals sign
Solving Linear Equations
The first thing we do is move any constants to the side without the variable
Addition undoes subtraction, subtraction undoes addition
The important thing to remember is that
what you do to one side of the equal sign, you have to do to the other
In this example, we will subtract 4 from both sides since it is added to the variable
4 – 4 = 0 and 1 – 4 = -3
So we are left with 5x = 3
the variable “x” is still not by itself, it has a 5 multiplied to it. We need to divide both sides by 5 in order to get rid of it.
The 5s will cancel out on the left hand side
What we are left with is x = -3/5. The variable “x” is by itself and this fraction does not simplify further so that is our solution
