Solving One-Variable Linear Equations

Solving One Variable Equations: 

"Linear equations are equations with a plain old variable like "x" rather than something more complicated like "x^2"

You've probably already solved linear equations; you just didn't know it. 

When solving a one variable equation, you need to "undo" whatever has been done to the variable. 

 A solution: a solution to an equation is a value or set of values that makes the equation true. 

For Example in the Equation: 

x + 2 = 3

the solution is x = 1, because 1 + 2 = 3. 

Lets Review: Additive Inverse: 

An additive number is something you add to a number to make it equal 0. 

2 + (-2) = 0

5 + -5 = 0

Multiplicative Inverse: 

A multiplicative inverse is something you multiple by another number to equal 1. 

2 X 1/2 = 1

You do this in order to get the variable by itself; in technical terms you are "isolating the variable."

For Example: x + 6 = -3

You first want to get the x on the left side by itself. So you will subtract the 6 to the right side. So now the equation looks like x = -3 - 6. So now we solve for x. -3 - 6 = -9. So x = -9.

Whatever you do to an equation,
do the   S A M E   thing
to   B O T H   sides of that equation!

Example: x - 3 = -5

Since you want to get x by itself, so you want to add 3 to both sides. 

x - 3 = -5

+3 = +3 

x = -2

Then the solution is x = -2. 

Lets solve this equation: 3x + 6 + 4x = 13

First we need to combine like terms: those terms are the 3x + 4x = 7x. 

So now the equation look like this: 7x + 6 = 13

So now to get the variable by itself we need to subtract the 6 from both sides. 

So we get 7x = 13 - 6

7x = 7

now we divide by 7 to get x by itself to both sides. 

So x = 1. 

Now we need to check our work

3 (1) + 6 + 4 (1) = 13

3 + 6 + 4 = 13

13 = 13. 

Therefore the solution is x = 1. 

Lets solve this equation: 3 - 5x = 18.

First we need to move the 3 to the other side to get x by itself, so lets subtract the 3 from both sides.

-5x = 18 - 3

-5x = 15. 

Now we need to divide by the -5 to get x by itself. 

x = 15 / -5

x = -3.

Now we need to check our work so we plug x = -3 back into the equation. 

3 - 5(-3) = 18

3 - (-15) = 18

18 = 18. 

Therefore the solution is x = -3.