Question

tutorial for solving linear equation

Answer 1

Strategy for Solving a Linear Equation


Note that your teacher or the book you are using may have worded these steps a little differently than I do, but it all boils down to the same concept - get your variable on one side and everything else on the other using inverse operations.

Step 1: Simplify each side, if needed.


This would involve things like removing ( ), removing fractions, removing decimals, and adding like terms.
To remove ( ): Just use the distributive property found in Tutorial 8: Properties of Real Numbers.

To remove fractions: Since fractions are another way to write division, and the inverse of divide is to multiply, you remove fractions by multiplying both sides by the LCD of all of your fractions. If you need a review on the LCD, go to Tutorial 3: Fractions.


Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.


Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.


Step 4: Check your answer.


I find this is the quickest and easiest way to approach linear equations.




Example 1: Solve the equation .




*Inverse of add. 10 is sub. 10


*Inverse of mult. by -3 is div. by -3



Be careful going from line 4 to line 5. Yes, there is a negative sign. But, the operation between the -3 and x is multiplication not subtraction. So if you were to add 3 to both sides you would have ended up with -3x + 3 instead of the desired x.
If you put 1 back in for x in the original problem you will see that 1 is the solution we are looking for.




Example 2: Solve the equation .



*Remove ( ) by using dist. prop.

*Get all x terms on one side

*Inverse of add. 3 is sub. 3



*Inverse of mult. by -1 is div. by -1




If you put 9 back in for x in the original problem you will see that 9 is the solution we are looking for.



Example 3: Solve the equation..



*To get rid of the fractions,
mult. both sides by the LCD of 4
*Get all the x terms on one side


*Inverse of add. 2 is sub. 2



*Inverse of mult. by -3 is div. by -3





If you put 4/3 back in for x in the original problem you will see that 4/3 is the solution we are looking for.



Example 4: Solve the equation .



*To get rid of the decimals,
mult. both sides by 100
*Get all the y terms on one side

*Inverse of sub. 20 is add 20



*Inverse of mult. by 20 is div. by 20





If you put 3/2 back in for y in the original problem you will see that 3/2 is the solution we are looking for.



Contradiction
A contradiction is an equation with one variable that has no solution.




Example 5: Solve the equation .




*Remove ( ) by using dist. prop.
*Get all the x terms on one side




Where did our variable, x, go??? It disappeared on us. Also note how we ended up with a FALSE statement, -1 is not equal to 12. This does not mean that x = 12 or x = -1.
Whenever your variable drops out AND you end up with a false statement, then after all of your hard work, there is NO SOLUTION.

So, the answer is no solution.





Identity
An identity is an equation with one variable
that has all numbers as a solution.




Example 6: Solve the equation .




*Remove ( ) by using dist. prop.
*Get all the x terms on one side




This time when our variable dropped out, we ended up with a TRUE statement. Whenever that happens your answer is ALL REAL NUMBERS.
So, the answer is all real numbers.

Answer 2

Never forget to mention the link from which you have taken this :
http://questgarden.com/46/00/5/070210132723/process.htm

it will be considered as plagiarism and is against code of conduct ..

Answer 3

wait... where'd you copy all this from?

Answer 4

right question ..@Ishaan94 that link :
http://questgarden.com/46/00/5/070210132723/process.htm

Answer 5

actually...it can also be found in http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut14_solve.htm

Answer 6

@best.shakir
Its ridiculous....... You should have better posted the link or should have mentioned it ........

@Ishaan94 @lgbasallote,. @mathslover You are right it is against the coc........

Answer 7

hey, stop it. it's not that he denied his act.

Answer 8

Well ok...........

What if he posts the link now.... ?