a tuxedo rental shop rents tuxedos with sleeve lengths from 20 inches to 40 inches. The shop says the length of the sleeves should be about 1.2 times a person's arm length. Write and solve a compound inequality that represents the arm lengths of people the shop does not provide tuxedos for.
fake your both wrong the answer is x is less than 16.66 or x is greater than 33.33
To solve this problem, we'll first need to set up two equations and then combine them into a compound inequality.
Let's say the length of a person's arm is represented by the variable "x". According to the shop, the length of the sleeves should be about 1.2 times a person's arm length. So, the acceptable sleeve length (SL) can be calculated as 1.2 times the arm length: SL = 1.2x.
Now, let's find the range of arm lengths for which the shop does not provide tuxedos. Since the shop only rents tuxedos with sleeve lengths from 20 inches to 40 inches, we can set up two inequalities to represent these boundaries:
20 ≤ SL ≤ 40
We can substitute SL with 1.2x in the inequalities:
20 ≤ 1.2x ≤ 40
Now we can solve this compound inequality:
20 ≤ 1.2x ≤ 40
Divide all parts of the inequality by 1.2:
20/1.2 ≤ (1.2x)/1.2 ≤ 40/1.2
16.67 ≤ x ≤ 33.33
Therefore, the compound inequality that represents the arm lengths of people the shop does not provide tuxedos for is:
16.67 ≤ x ≤ 33.33
In conclusion, the shop does not provide tuxedos for people with arm lengths between 16.67 inches and 33.33 inches.
well, the people who do get tuxes satisfy
20 <= 1.2x <= 40
So, solve that for x and then take everything else.