Question:
Solve for x: . Fill in both values for x below. Write the greater value for x in the first column.
Answer:
and
are the values for x.
Explanation:
The equation is
Subtracting both sides by 7,
Dividing both sides by 12,
Now, we shall write the equation by removing modulus by adding plus and minus on the other side of the equation.
or
Solving the equation , we get,
or
Thus, the solutions are and
Problem 1
Answers:
Domain:
Range:
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Explanation:
The domain is the set of allowed x inputs of a function. The smallest x value we can use is x = -3 (note the very left-most point of the graph). The right-most point involves x = 5, but we can't actually use this x value due to the open hole. So that's why we don't have "or equal to" attached to the 5.
The range is the set of possible y outputs. The lowest we can go is y = -4, but we don't include this as part of the range. The largest y can get is y = 3. So the range is
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Problem 2
Answers:
Domain:
Range:
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Explanation:
We use the same idea as in problem 1. Both endpoints are open holes, so we don't include them as part of the domain and range. For instance, we can't include x = 4 but we can get closer and closer to it. The same idea applies to the range as well.
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Problem 3
Answers:
Domain:
Range:
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Explanation:
The same idea applies as used earlier. This time we include both endpoints, so we have "or equal to" as part of each inequality sign.