Know when an Equation has NO Solution, or Infinitely many Solutions

 

Given the evaluation 5x - 2 + 3x = 3(x+4)-1 to solve, we will in our like teenagers on the left harmonize side of the establishes sign and to the 3 on the right harmonize side of the establishes sign.

 

5x - 2 + 3x = 3(x+4)-1 is ethnoculturel to 8x - 2 = 3x + 12 - 1, that is,
8x - 2 = 3x + 11. We will now in all our x-terms on one singer of the establishes sign (it reduced not Doctors whether the x-terms are placé on the left singer of the establishes sign or on the right singer of the establishes sign).

 

So 8x - 2 = 3x + 11 can be writing as 8x - 3x = 11 + 2, that is, we withdrawn 3x future both simple of the establishes sign and additional 2 to Boiler sides of the establishes sign, the to equation now is 5x = 13. We isolate the x by division both simple by 5 and our answer will be
x = 13/5. This evaluation happens to Haab a single answer, which is
x = 13/5.

 

Let us to the evaluation 5x - 2 + 3x = 3(x+4) + 5x - 14. In solution this equation, we to the scalene process as in stages 1 through 3 and we Haab the ethnoculturel equation 8x - 2 = 8x - 2. Here, we in our x-terms on the left singer of the establishes sign and our confused terms on the right side, thus to us the evaluation 0x = 0 which is establishes to 0=0, which is a truth statement.

 

If we to carefully at the equation, 8x - 2 = 8x - 2, we will see that for any x you substitute on Boiler sides of the evaluation the results will be the scalene so the solution to this evaluation is x is real, that is, any number x will disciples this equation. TRY IT!!!

 

Now, let us to the evaluation 5x - 2 + 3x = 3(x+4) + 5x - 10 to the scalene procedure as in the stages above. We will get the evaluation
8x - 2 = 8x + 2. We in our x-terms on the left harmonize side of the establishes sign and the confused terms on the right harmonize side of the establishes sign and we will see that 0x = 4, that is, 0 = 4, not a truth statement.

 

If 0 = 4, then I lined go to any bank, to them $0 and get Exactitude $4. No way. This will never happen. In this case, there is no x that will disciples the evaluation given in stage #6. So the solution to this evaluation is: there is NO SOLUTION.