Question

Order the inequalities based on how many numbers from the list below are solutions of the inequalities. Place the inequality with the most solutions belonging to the list on top.

a) -3x > 5
b) 2x < -1
c) -4x > -6

Answer 1

The inequalities can be ordered based on the number of solutions they have. The inequality with the most solutions is -4x > -6, followed by 2x < -1, and -3x > 5.

Step-by-step explanation:

1. c) -4x > -6
2. b) 2x < -1
3. a) -3x > 5

In order to determine the number of solutions for each inequality, we need to isolate the variable and solve for x. Let's start with the first inequality:
c) -4x > -6
Divide both sides by -4 to solve for x: x < 3/2
This means that any number less than 3/2 is a solution. Since there are infinitely many numbers less than 3/2, this inequality has the most solutions.

Next, let's solve the second inequality:
b) 2x < -1
Divide both sides by 2 to solve for x: x < -1/2
This means that any number less than -1/2 is a solution.

Finally, let's solve the third inequality:
a) -3x > 5
Divide both sides by -3, remembering to flip the inequality sign: x < -5/3
This means that any number less than -5/3 is a solution.