Nine less than three times a number is greater or equal to eight more than twice the same number

Answer 1

Hello Turner,

Okay, so first thing we want to do is to create some expressions which will reflect these numbers, especially given the fact that they are not given in the problem, okay?

Therefore,

Let x ≥ the number. We need only use x for the number since the problem asks for the same number twice.

3x - 9 ≥ 2x + 8

This is clearly an inequality, and we need to solve it as such. Please note: Nine less (means subtract nine) than three times (which means 3 times whatever variable you wish to assign it) is greater or equal to (means it is equal to or greater) to eight more than twice (2 ties the same variable we assigned) the same number. You good so far? Great!

Now we need to solve the inequality.

3x - 9 ≥ 2x + 8 <-------Add eight to each side of the inequality

3x ≥ 2x + 17 <-------Subtract 2x from both sides

x ≥ 17

What this means is that every value you substitute for x should be ≥ 17. You can check this out on your own, however, the solution checks and is therefore valid.

As a tutor, I do feel it my obligation to share the following information about inequalities. First, they are all solved like equations with a few exceptions. We flip the direction of the inequality sign when when we multiply or divide both sides of the equation by a negative number. In addition, when working with absolute values we change the direction of the sign.

I hope I have provided you with assistance today, as I wish you and yours a Happy Holiday Season. If you need further clarity, wish to provide feedback, or have additional questions, please feel free to reach out to me through the Wyzant system. If you are in need of one on one tutoring, please do not hesitate to reach out to me or any tutor. Best!