SOLUTION: What is the solution to the equation |x - 3| = 14? What is the solution to the equation |2x - 3| + 4 = 17? What is the solution to the equation |x - 10| - 4 = 2x? What is the so

Algebra ->  Absolute-value -> SOLUTION: What is the solution to the equation |x - 3| = 14? What is the solution to the equation |2x - 3| + 4 = 17? What is the solution to the equation |x - 10| - 4 = 2x? What is the so      Log On


   

Question 789971: What is the solution to the equation |x - 3| = 14?
What is the solution to the equation |2x - 3| + 4 = 17?
What is the solution to the equation |x - 10| - 4 = 2x?
What is the solution to the equation |3x - 15| = 0?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Most of these are almost the same format.
Treat the absolute value as a variable; you could also factor some of them.... actually you can factor ONE of them.

Consider the possibility that the expression inside the absolute value can be positive, or less than or equal to zero. Solve for each case.

For some expression |a-b|,
if a-b%3E=0 then |a-b|=a-b.
if a-b%3C0 then |a-b|=-1(a-b)=b-a

Looking at your third sample,abs%28x-10%29-4=2x
abs%28x-10%29=2x%2B4
If x-10%3E=0 then you have x-10=2x%2B4
x-2x=10%2B4
-x=14
highlight%28x=-14%29
If x-10%3C0 then you have -x%2B10=2x%2B4
-x-2x=-10%2B4
-3x=-6
highlight%28x=2%29

Conclusion on this one is x is either 2 or -14.