I posted this earlier but it didn't get answered. So I'm posting it again with hopes that, this time, it will be answered.
Please solve for x: |x-6|>7
I got x=6 as a final answer, but that doesn't make sense because 6 is not greater than 7. Please help!! Thanks :) No one has answered this question yet
To solve the inequality |x-6| > 7, we can break it down into two cases based on the absolute value function.
Case 1: (x-6) > 7
To solve this, we will isolate x.
Add 6 to both sides:
x - 6 + 6 > 7 + 6
x > 13
Case 2: -(x-6) > 7
Multiply both sides by -1 (effectively reversing the inequality):
x - 6 < -7
Add 6 to both sides:
x - 6 + 6 < -7 + 6
x < -1
So, the solution to the inequality |x-6| > 7 is x < -1 or x > 13.
In your attempt, it seems like you have considered only one of the cases and found x = 6. However, that is not the correct solution. To solve this type of inequality, we need to consider both cases and find the intersection of the solutions.