Solve the absolute value equation.
I I will represent absolute value
I 2x-4 I -1= 11
Would the solutions be x=8 and x= -4?
* Algebra - Reiny, Tuesday, October 13, 2009 at 5:41pm
I just mentally tested x=8.
It did not work in your equation
take the -1 to the other side and follow the steps I just showed you in the previous problem
I did take the -1 to the other side. Here's exactly how I did it:
I 2x-4 I -1=11
added 1 to both sides
That came out to:
I 2x-4 I =12
I separated it into
2x-4=12 and 2x-4=-12
add 4 to both sides of each
2x=16 and 2x=-8
divide each by two
x=8 and x= -4
What part of my figuring is off?
I am sorry, you are right!!!!!
Three strikes, I guess I am out
Your process of solving the absolute value equation seems correct. However, the solutions you calculated, x=8 and x=-4, are incorrect. Let's go through the solution again step by step:
Given equation: |2x-4| - 1 = 11
Step 1: Add 1 to both sides of the equation:
|2x-4| = 12
Step 2: Separate the equation into two cases, one for each possible sign of the absolute value expression:
Case 1: 2x-4 = 12
Solve for x:
2x = 16
x = 8
Case 2: -(2x-4) = 12
Solve for x:
-2x + 4 = 12
-2x = 8
x = -4
So the correct solutions to the absolute value equation are x = 8 and x = -4. It seems like you made a typo or miscalculation when handling the second case, resulting in an incorrect solution.
It's always a good idea to double-check your calculations to avoid mistakes, especially when dealing with absolute value equations.