solve
absolute value 2x-20 absolute value=absolute value 9x+ ansolute value 15
|2x-20|=|9x+15|
Following the definition of the absolute function, we have:
|2x-20|=2x-20 when 2x-20≥0, and
|2x-20|=-(2x-20) when 2x-20<0
and a similar relationship exists for the right hand side.
For this particular case, solving the following equations for x will cover all cases:
2x-20=9x+15 ...(1), and
2x-20=-(9x+15) ...(2)
The following graphic depicts the solutions to (1) and (2):
http://img228.imageshack.us/img228/2189/1285109962.png
To solve the absolute value equation |2x - 20| = |9x + 15|, we need to consider the two possible cases:
Case 1: (2x - 20) = (9x + 15)
In this case, we remove the absolute value symbols and solve for x:
2x - 20 = 9x + 15
Subtract 2x from both sides:
-20 = 7x + 15
Subtract 15 from both sides:
-35 = 7x
Divide by 7 to isolate x:
x = -5
Case 2: -(2x - 20) = |9x + 15|
In this case, we take the negative value of (2x - 20) and compare it to |9x + 15|:
-(2x - 20) = 9x + 15
Distribute the negative sign:
-2x + 20 = 9x + 15
Subtract 20 from both sides:
-2x = 9x - 5
Add 2x to both sides:
0 = 11x - 5
Add 5 to both sides:
5 = 11x
Divide by 11 to isolate x:
x = 5/11
Thus, the solution to the absolute value equation |2x - 20| = |9x + 15| is x = -5 and x = 5/11.