Answer:
The answer to the problem is 5
Step-by-step explanation:
The sum of twice a number y and 5 is at most 15" can be translated mathematically into the following inequality:
2y + 5 ≤ 15 since the sum, 2y + 5, is at most 15 but could be less than 15.
To solve this inequality for n, proceed as follows:
First, subtract 5 from both sides of the inequality as you would in solving an equation:
2y + 5 - 5 ≤ 15 - 5
2y + 0 ≤ 10
2y ≤ 10
Now, to finally solve the inequality for the variable y, divide both sides of the inequality by 2 as you would in solving an equation:
(2y)/2 ≤ 10/2
(2/2)y ≤ 10/2
(1)y ≤ 5
n ≤ 5 which is all real number less than or equal to 5.
Test Values (y = -1/2, 0, 3, 5, and n = 7):
For y = -1/2:
2y + 5 ≤ 15
2(-1/2) + 5 ≤ 15
-1 + 5 ≤ 15
-4 ≤ 15 (TRUE)
For y = 0:
2y + 5 ≤ 15
2(0) + 5 ≤ 15
0 + 5 ≤ 15
5 ≤ 15 (TRUE)
For y = 3:
2y + 5 ≤ 15
2(3) + 5 ≤ 15
6 + 5 ≤ 15
11 ≤ 15 (TRUE)
For y = 5:
2y + 5 ≤ 15
2(5) + 5 ≤ 15
10 + 5 ≤ 15
15 ≤ 15 (TRUE)
For y = 7:
2y + 5 ≤ 15
2(7) + 5 ≤ 15
14 + 5 ≤ 15
19 ≤ 15 (FALSE)
Therefore, the possible values for y which will make the relevant inequality, 2n + 5 ≤ 15, a true statement are:
{y | y is a real number and y ≤ 5}
