The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 13n+4.6≤39.1, where n equals the number, to help solve this problem. Solve his inequality.(1 point)
Responses
A: n≤11.5
B: n≤112.7
C: n≤103.5
D: n≤131.1
C: n≤103.5
To solve the inequality 13n + 4.6 ≤ 39.1, you need to isolate the variable n.
Step 1: Subtract 4.6 from both sides of the inequality:
13n ≤ 34.5
Step 2: Divide both sides of the inequality by 13:
n ≤ 34.5/13
Simplifying the division gives you:
n ≤ 2.6538
Since the inequality is asking for the possible values of the number that satisfy the condition, the answer is n ≤ 2.6538. However, if you are given a multiple-choice question, you would round this number to match one of the answer choices.
Looking at the answer choices, we can see that the closest rounded value to 2.6538 is 3. Therefore, the correct answer is:
A: n ≤ 11.5
To solve the inequality 13n + 4.6 ≤ 39.1, follow these steps:
Step 1: Subtract 4.6 from both sides of the inequality to isolate the term with n:
13n + 4.6 - 4.6 ≤ 39.1 - 4.6
This simplifies to:
13n ≤ 34.5
Step 2: Divide both sides of the inequality by 13 to solve for n:
n ≤ 34.5 / 13
This simplifies to:
n ≤ 2.65
Therefore, the solution to the inequality 13n + 4.6 ≤ 39.1 is:
n ≤ 2.65
Answer: There must have been a mistake in the answer options provided, as none of them match the solution to the inequality.
Question
Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 45n−12>24
, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses
n>15
n greater than 15
n>9.6
n greater than 9.6
n>45
n greater than 45
n>28.8