Question

PLEASE HELP! I NEED TO GET THIS DONE BEFORE TOMORROW!!

Li’s family has a coupon for $49 off a stay at any hotel. They do not want to spend more than $150 in all. An inequality representing this situation is x - ≤ 150. Explain how you would graph this inequality. What will be included in the solution set in the context of the problem?

Answer 1

The solution set includes all numbers less than or equal to 199. I would draw a closed circle at 199 and draw an arrow pointing to the left. In the context of the problem, only money values greater than or equal to 0 make sense.

Answer 2

Here, x represents the money spent by them,

Since, they have already a coupon of $ 49 off,

Thus, their total spending = x - 49

According to the question,

They do not want to spend more than $150 in all.

⇒ x - 49 ≤ 150,

⇒ x ≤ 150 + 49

⇒ x ≤ 199

Since, spending must be greater than equal to 0,

⇒ 0 ≤ x ≤ 199

Thus, the solution set in the context of the problem is [0, 199]

Hence, we can graph the given inequality by plotting [0, 199] on the number line. ( shown below )