Solve the equation. What does this = please? Thanks :)
|n – 6| = |1 – n|
n-6 = 1-n --> n = 3.5
-n+6 = 1-n --> n = no value possible
n-6 = -1+n ---> no value possible
-n+6 = -1+n ---> n=3.5
well, check this around n = 3.5
if n = 3.5
|3.5-6| = |1-3.5| = 2.5 check
Would 7/2 be somthing that makes the equation =?
These are my choices:
{7/2}
{-5/2}
{7}
(“Empty set”)
None of the above
To solve the equation |n – 6| = |1 – n|, you need to consider two cases: when the expression inside the absolute value bars is positive and when it is negative.
1. When n - 6 is positive:
In this case, the equation becomes n - 6 = 1 - n. Simplify it by adding n to both sides:
n - 6 + n = 1 - n + n
2n - 6 = 1
Next, add 6 to both sides to isolate the variable:
2n - 6 + 6 = 1 + 6
2n = 7
Finally, divide both sides by 2:
2n/2 = 7/2
n = 7/2
So, one possible solution is n = 7/2.
2. When n - 6 is negative:
In this case, we need to change the sign of the expression inside the absolute value bars. The equation becomes -(n - 6) = 1 - n. Simplify it by distributing the negative sign:
-n + 6 = 1 - n
The variable n cancels out, leaving you with 6 = 1.
However, this equation is not true since 6 does not equal 1. Thus, there are no solutions in this case.
Hence, the only solution is n = 7/2.