its to hArd I don't know what I'm doing.
Let's talk about the steps to solve single variable equations. (3x + 15 + 5x = -1)
1. Combine LIKE terms on the same side of the equal sign
That means add apples to apples and oranges to oranges. In the equation given above equation there are 4 terms: 3x, 15, 5x and -1.
On the left side of the equal sign 3x and 5x are alike...so we add them. 3x + 5x = 8x
8x + 15 = -1
2. Get all the X terms on one side of the equal sign!
In this problem all of the X terms are on the left side of the equal sign, however in another problem you might have X terms on both the left and the right side. You can move them to either side, but in general the best side to move them to is the side which keeps the coefficient on the X term positive. Currently the coefficient on the X term is 8 and positive. Moving it to the right side would make it negative.
Use INVERSE OPERATIONS of addition and subtracton (listed below in next step) to achieve this.
3. ISOLATE the X term.
Now that there is only 1 X term in your equation, we need to move everything else away from it...e.g. now that we have gathered all of our apples, we need to move the oranges, bananas and strawberries away from it so that the apples are ISOLATED...or by themselves.
USE INVERSE OPERATIONS to accomplish this...
- If the operation was addition, use subtraction
- If the operation was subtraction, use addition
- If the operation was multiplication, use division
- If the operation was division, use multiplication
8x + 15 - 15 = (-1) - 15
8x + (15 - 15) = (-1) + (-15) <-- you can always change subtraction to addition like this
8x = -16
The X is now isolated...it is on the left side of the the equal sign...all by it's lonesome.
4. Make the coefficient on the X term 1 (MUST BE POSITIVE).
Currently the coefficient on the X term is 8, but since we want it to be 1, we should divide 8x by its current coefficient because 8÷8 =1. REMEMBER, whatever we do to one side we must do to the other!
(8x) ÷ 8 = -16 ÷ 8
x = -2
5. ALWAYS, ALWAYS CHECK YOUR ANSWER...
Algebra is the only class where a math teacher can not go easy on you while grading and my favorite math teacher showed me that the difference between an A and a B is this step...because you can prove that your answer is CORRECT!
Check your answer by replace X with the derived value of 2 in the ORIGINAL equation. I know it may seem easier to plug it into 8x + 15 = -1 or 8x = -16, but these are INTERMEDIATE STEPS and if you made a mistake between the ORIGINAL equation and these steps you won't have proven that your answer is correct. So instead we use:
3x + 15 + 5x = -1
3(-2) + 15 + 5(-2) = -1
To complete this problem we will need to use Order of Operation (PEMDAS)...just remember use PEMDAS left to right ALWAYS and you'll never go wrong.
-6 + 15 + (-10) = -1
(-6 +15) + (-10) = -1
9 + (-10) = -1
-1 = -1 <-- We have proven that x= -2 is the solution to this problem.
The steps I have outlined above can be used for any single variable equation no matter how many terms exist in the original equation. I like to use parentheses () around negative numbers so that I don't lose them...it helps me cut down on the amount of rework when my check tells me that my answer is incorrect.
It is simple: Keep all the unknowns (x 's) on the Left Hand Side (LHS) and move all the known to the Right Hand Side (RHS), so we have:
8x = -16
or x = -2.
now check your answer, by substituting the value of x in the first equation:
3x +15+5x = -1
So, LHS becomes (with x =-2): 3*-2+15+5*-2 = -1 which is what RHS is, so the answer is correct.
This is the way to check all your algebra equations that you solve for an unknown (x).
Hope you have a better understanding!