What value of x is in the solution set of 3 (x-4)> 5x+2

Question

What value of x is in this solution 3 (x-4)> 5x+2

 

 

-10

 

-5

 

5

 

10

I don't know how to solve this at all and I don't get the question.

Answer 1

Hi Taylor,

 

You solve this just like you would solve an equation.  See the steps below.

 

3(x-4) > 5x+2

 

 

First Multiply 3(x-4).  Multiply 3 by each number in the parentheses.  First 3 * x then 3 * -4.  That leaves you with 3x - 12.  see below.

 

  3x-12 > 5x+2

 

Next get the variables on the same side (of the > sign).  Remember whatever you do to one side you need to do to the other side so we will subtract 5x from both sides.

 

   3x -12 > 5x +2

  -5x         -5x

 

That leaves us with..

 

  -2x - 12 > 2

 

Now lets get the numbers on one side by adding 12 to both sides.  Adding 12 to the side with -12 will get rid of the number from the left side and adding 12 to the right side makes it 14.

 

  -2x - 12 > 2

        +12  +12

 

That leaves us with...

 

  -2x > 14

 

Now lets get x by itself by dividing by -2, again remember what we do to one side we need to do to the other.

 

  -2x > 14

   -2     -2

 

When you divide both sides by a negative number it reverses the sign from > to < That leaves us with....

  x < -7

 

So the answer is any number less than -7, so -10 part of the solution set.

 

 

Hope this helped.

 

Matt