Inequality problem: solve 2(x - 2) < 2/3x for X

[LisaPersad]

2(x - 2) < 2/3x

solve for X

My work:

2(x - 2) < 2/3x
2x - 4 < 2/3x
2x - 2/3x < 4
6x - 2x/3 < 4
4x/3 < 4
3(4x/3) < 4(3)
4x < 12
4x/4 < 12/4
x< 3

Is this the correct answer? I solved for X by isolating the X.
This makes sense to me but I am not sure if it is correct.
Can you please tell me if this is correct.

Lisa

 

[Loren]

Re: Inequality problem

2(x - 2) < 2/3x <<<This means \(\displaystyle 2(x-2) < \frac{2}{3}x\)

solve for X

My work:

2(x - 2) < 2/3x
2x - 4 < 2/3x
2x - 2/3x < 4
6x - 2x/3 < 4 <<< 3(2x - 2/3x) < 3(4) becomes 6x -2x < 12. Take it from there.
4x/3 < 4
3(4x/3) < 4(3)
4x < 12
4x/4 < 12/4
x< 3

You ended up with the correct result but your means of getting there is flawed. You make statements that are not true in your mechanics. I think your thinking is okay. But, instead of doing a particular thing to one side of the inequality, then doing that same thing to the other side and putting each step on a separate line, you should do both of those things at the same time. Here is each itsy-bitsy step. With practice, you will be able to combine some of these.

2(x - 2) < 2/3x
2x - 4 < 2/3x
2x - 4 - 2/3x < 2/3x - 2/3x
2x - 4 - 2/3x < 0
2x - 4 - 2/3x + 4 < 0 + 4
2x - 2/3x < 4
3(2x - 2/3x) < 3(4)
6x - 2x < 12
4x < 12
4x/4 < 12/4
x < 3

Here are the steps I would take.
2(x - 2) < 2/3x
2x-4 < 2/3x
3(2x-4) <3(2/3x)
6x - 12 < 2x
6x - 2x < 12
4x < 12
x < 3