How do you find the solution set for the equation |x-6|=7?
Note that we define the absolute value function as
so we consider two cases:
As these cases account for all possibilities, we have found all possible solutions.
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To find the solution set for the equation (|x - 6| = 7), you can set up two separate equations based on the absolute value:
- (x - 6 = 7)
- (x - 6 = -7)
Solve each equation separately to find the solutions for (x).
- For (x - 6 = 7), add 6 to both sides to get (x = 13).
- For (x - 6 = -7), add 6 to both sides to get (x = -1).
So, the solution set for the equation (|x - 6| = 7) is ({13, -1}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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