Three times the square of a number is greater than a second number. The square of the second number increased by 6 is greater than the first number. Which system of inequalities represents these criteria?

Given:

Three times the square of a number is greater than a second number.

The square of the second number increased by 6 is greater than the first number.

To find:

The system of inequalities represents these criteria.

Solution:

Let the first number be x and the second number be y.

Three times the square of a number is greater than a second number.

          ...(i)

The square of the second number increased by 6 is greater than the first number.

      ...(ii)

Therefore, the system of inequalities represents these criteria has inequalities and , where x is first number and y is second number.

Hey there!

To find the opposite of a number, you switch its sign, and to do so, you would multiply by -1. This gives us the equation below.

n=-n+96

To find our number, we need to isolate all of our n's on one side of the equation. Let's try adding n to both sides.

2n=96

We divide both sides by 2.

n=48

As you can see, the opposite of 48 is -48, and 48 is 96 more than -48.

Therefore, our number is 48.

I hope this helps!