5(2n + 4) - 3(4n - 6) = 2(20 - n)
I solved this equation and this is what I got.
10n + 20 - 12n + 18 = 40 - 2n
-2n + 38 = 40 -2n
38 ≠ 40
What does this mean?
Thank you!
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
If you end up with no variables, and the remaining statement is false, like in your case ----> the equation has no solution.
If you end up with no variables, and the remaining statement is true ---> the equation is true for any value of the variable. It would be an "identity"
Based on the steps you provided, it appears that you simplified the equation correctly until you arrived at the statement "-2n + 38 = 40 - 2n". However, notice that there are terms with "-2n" on both sides of the equation. This means that the variable "n" cancels out when you subtract "-2n" from both sides, resulting in the statement "38 = 40".
Since "38" is not equal to "40", this means that there is no solution to the given equation. In other words, there is no value of "n" that satisfies the equation. This type of equation is called a contradiction, where the statement is false for all values of the variable.