Give an example of two inequalities that are equivalent inequalities. Explain your reasoning.

3x + 5 > 20

-2x + 8 < -2

Step-by-step explanation:

Start with

x > 5

Now we will do several legal operations to both sides of the inequality to come up with two equivalent inequalities.

x > 5

Multiply both sides by 3:

3x > 15

Add 5 to both sides:

3x + 5 > 20       First inequality

Start again with

x > 5

Multiply both sides by -2. Remember to change the direction of the inequality sign.

-2x < -10

Add 8 to both sides.

-2x + 8 < -2      Second inequality

The two equivalent inequalities are:

3x + 5 > 20

-2x + 8 < -2

These inequalities are equivalent inequalities because both of them have the same solution, x > 5.