Question

Which integers satisfy the inequality 2x + 9 < 12?

A) 1, 2, 3
B) 0, 1, 2
C) -3, -2, -1
D) -4, -3, -2

Answer 1

Integers that satisfy the inequality 2x + 9 < 12 are those which are less than 1.5. By finding the integers less than 1.5, we conclude that the correct answer is option C) -3, -2, -1.

Step-by-step explanation:

To find which integers satisfy the inequality 2x + 9 < 12, we first isolate the variable x by subtracting 9 from both sides of the inequality:

2x + 9 - 9 < 12 - 9
2x < 3

Next, we divide both sides by 2 to solve for x:

2x / 2 < 3 / 2
x < 1.5

So x must be less than 1.5. Since we are looking for integers, this means x can only be 1 or any integer less than 1. The list of integers that satisfy this inequality is -∞, ..., -4, -3, -2, -1, 0, 1. The correct answer, which includes only the reasonable options given -3, -2, and -1, is:

Option C) -3, -2, -1