What are all possible values of x that satisfy the inequality

Question

What are all possible values of x that satisfy the inequality 12-3x<18

Answer 1

Hi...Grace from Mccall, ID...hope you have a great day at school.

This is a great Algebra question...inequalities...every student's favorite? NOT!!

Anyway, I'm here to help, I will help you get started, however I won't solve the problem for you, but give you the rules so you can solve it. As a teacher I would also expect you to then GRAPH you solution with a numberline. I would make it a habit to do this with EVERY inequality kind of problem. I gave my students extra credit when they did and when they didn't, they lost a point. It helps you understand the difference between the solutions for inequalities as compared to equations.

 Solving Algebraic equations you know whatever you do on one side of the equation, you do the same on the other side of the equation. You should know that this may changed the appearance of the equation, but it does not change the value of the equation.

Now the second hint, is that with inequalities, you follow the same rules when solving with certain exceptions. The inequality sign does not change when you add or subtract on either side. However when you multiply or divide with a negative value, in change, invert the inequality sign.

Here are some examples:

    3x  +  2  = 14   you should know how to solve this

    3x + 2 -2 = 14 - 2

    3x + 0 = 12

     3x/3  = 12/3

        x    =   4    check you answer    3(4) + 2 = 12 + 2 = 14  Right?

 

      3x + 2 > 17     We'll do the same thing.

      3x + 2 - 2 > 17  - 2

      3x + 0 > 15

        3x/3  >   15/3

         x     >    5   check your answer   since x has to be > 5, let x be 6

        3(6) + 2 > 13     18 + 2 > 13       20  > 13   that is correct, Right?

        This time try letting x be 4, is the inequality true?

 

NOW...let's change the inequality slightly:

      -2x - 5 <  23    follow the same rules to begin with   

      -2x - 5 + 5 < 23 + 5

      -2x - 0 < 28

      -2x/-2  <  28/-2    You understand where we are at...RIGHT? NOW...

      -2x/-2  >  28/-2   Since we divided by a (-) number, change the sign

           x    >    -14     Now, confirm you answer by checking. Let x = -14

      -2(-14) - 5 < 23     28 - 5 < 23    23 < 23  this is not a true statement because 23 isn't less than 23. So let's try 0 because is greater than -14

        -2(0) - 5 < 23     0 - 5 < 23     -5 < 23  so -5 is less than 23

Now you have the tools to answer your question. Try this, if you still need help. Contact me on Wyzant. Once you know and practice these rules, you will be a pro at these.