SOLUTION: A. Translate. (Do not simplify or solve.) Eight more than k exceeds 23. B. Solve. (Simplify your answer completely.) C. Write the solution in interval notation. D.Graph o

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Question 1190203: A. Translate. (Do not simplify or solve.)
Eight more than k exceeds 23.
B. Solve. (Simplify your answer completely.)
C. Write the solution in interval notation.
D.Graph on the number line.

Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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A. Translate. (Do not simplify or solve.)
Eight more than k exceeds 23.
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Literally
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Part A

Answer:

The "k+8" part represents "8 more than k".
Whatever k is, add on 8. This sum exceeds 23, meaning it's larger than 23.

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Part B

To isolate k, we subtract 8 from both sides. We solve the inequality just like it was an equation. The inequality sign won't flip.





is the answer

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Part C

The result of part B was k > 15

This is the same as 15 < k. I swapped both sides and flipped the inequality sign.

We can further say 15 < k < infinity to tell us that the interval starts at 15 and "ends" at positive infinity.
I put "ends" in quotes because the interval doesn't really end of course. It goes on forever to the right.

We aren't including either endpoint, so we use parenthesis for each endpoint.

Answer: (15, infinity)
Use the infinity symbol in place of the word if necessary.
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Part D

Follow these steps
  1. Draw a number line.
  2. Plot an open hole at 15.
  3. Shade to the right.
This visually describes every value of k larger than 15.
The value k = 15 itself is not part of the solution set.
This is because k > 15 would update to 15 > 15 which is false.
No number is larger than itself. This is why we need the open hole at the endpoint.
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