in which of the given sets of numbers are all the numbers solution of 18 + 2x > 36?

Answer 1

The question is asking for numbers that satisfy the inequality 18 + 2x > 36.

Let's solve this inequality to find out which set of numbers satisfy it:

18 + 2x > 36
Subtract 18 from both sides:
2x > 18
Divide both sides by 2:
x > 9

So, any number greater than 9 would satisfy the inequality 18 + 2x > 36.

Let's check each set of numbers:

a) {6, 10, 12, 15}
For x = 6, 18 + 2(6) = 18 + 12 = 30 which is less than 36, so 6 is not a solution.
For x = 10, 18 + 2(10) = 18 + 20 = 38 which is greater than 36, so 10 is a solution.
For x = 12, 18 + 2(12) = 18 + 24 = 42 which is greater than 36, so 12 is a solution.
For x = 15, 18 + 2(15) = 18 + 30 = 48 which is greater than 36, so 15 is a solution.

All the numbers in set a) {6, 10, 12, 15} are not solutions as only 10, 12, and 15 are solutions.

b) {8, 9, 10, 11}
For x = 8, 18 + 2(8) = 18 + 16 = 34 which is less than 36, so 8 is not a solution.
For x = 9, 18 + 2(9) = 18 + 18 = 36 which is equal to 36, so 9 is not a solution.
For x = 10, 18 + 2(10) = 18 + 20 = 38 which is greater than 36, so 10 is a solution.
For x = 11, 18 + 2(11) = 18 + 22 = 40 which is greater than 36, so 11 is a solution.

In set b) {8, 9, 10, 11}, only 10 and 11 are solutions.

Therefore, all the numbers that are solutions to the inequality 18 + 2x > 36 are {10, 11} from the set b) {8, 9, 10, 11}.