I posted this last night 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 :)
To solve the inequality |x-6|>7, you need to consider two cases:
Case 1: (x-6) > 7
In this case, isolate x by adding 6 to both sides of the inequality:
x - 6 + 6 > 7 + 6
x > 13
Case 2: (x-6) < -7
In this case, isolate x by adding 6 to both sides of the inequality:
x - 6 + 6 < -7 + 6
x < -1
So the solution to the inequality |x-6|>7 is x < -1 or x > 13. Therefore, your final answer of x=6 is not correct.
To visually understand why x=6 is not a valid solution, consider the absolute value function. |x-6| represents the distance between x and 6 on the number line. For |x-6| to be greater than 7, x must be at least 7 units away from 6 in either the positive or negative direction. Therefore, x cannot be equal to 6.
Hope this helps clarify the solution process for you!