x is a real number satisfying the equation |x−20|+12=x. What is the value of x?
16 :)
I need to read up on this stuff, and figure out how to solve them.
To find the value of x that satisfies the equation |x - 20| + 12 = x, we need to analyze two cases: when x - 20 is positive and when x - 20 is negative.
Case 1: (x - 20) is positive or greater than 0
In this case, |x - 20| simplifies to (x - 20), so we can rewrite the equation as:
(x - 20) + 12 = x
Simplifying further:
x - 20 + 12 = x
x - 8 = x
Now, subtracting x from both sides:
-x - 8 = 0
Adding x to both sides:
-x + x - 8 = x
-8 = 0
This equation is not true, meaning there is no solution in this case.
Case 2: (x - 20) is negative or less than 0
In this case, |x - 20| simplifies to -(x - 20) or -(20 - x), so we can rewrite the equation as:
-(x - 20) + 12 = x
Simplifying further:
- x + 20 + 12 = x
32 = x + x
32 = 2x
Dividing both sides by 2, we get:
16 = x
Therefore, the real number x that satisfies the equation |x - 20| + 12 = x is x = 16.