A student keeps track of his target heart rate when he is exercising. The range for the number of heart beats per minute R for someone his age is /R-136/ less than or equal to 20. Determine the solution to the inequality. I believe the answer is: (116,156). Am I correct?

Question

A student keeps track of his target heart rate when he is exercising. The range for the number of heart beats per minute R for someone his age is /R-136/ less than or equal to 20. Determine the solution to the inequality. I believe the answer is: (116,156). Am I correct?

/R-136/ less than or equal to 20,
-20 less than or equal R-136 less than or equal to 20, leaves 116 less than or equal to R less than or equal to 156.

Answer 1

I read that as

|R-136| ≤ 20
-20 ≤ R-136 ≤ 20
add 136
116 ≤ R ≤ 156

you are correct

Answer 2

Yes, you are correct. To solve the inequality /R-136/ ≤ 20, you correctly applied the definition of absolute value to isolate the expression R-136. By establishing the compound inequality -20 ≤ R-136 ≤ 20 and then simplifying it, you obtained 116 ≤ R ≤ 156 as the solution range. Therefore, the correct solution to the inequality is (116, 156), as you stated.