Is the inequality below sometimes, always, or never true?

-2(2x + 9) -4x + 9
I want a simple explanation please. I'm having a lot of trouble with math and I need help understanding.

Question

Is the inequality below sometimes, always, or never true?

-2(2x + 9) > -4x + 9
I want a simple explanation please. I'm having a lot of trouble with math and I need help understanding.

misty1212 · Answer

HI!!

anonymous · Answer

Hello. I'm not asking for the answer because I know that's not allowed I just need someone to explain this to me.

misty1212 · Answer

probably the best bet is to multiply out first on the left 
i.e. distribute the $-2$

misty1212 · Answer

$$-2(2x + 9) > -4x + 9\
-4x-18>-4x+9$$

misty1212 · Answer

this is kind of a trick question, but lets keep going

anonymous · Answer

Trying to understand... The textbook hardly explains anything so I'm struggling

misty1212 · Answer

this is kind of a trick question, but lets keep going

anonymous · Answer

Okay thanks. Explain it to me as easy as you can. Usually I will be able to understand when i analyze it a few times and really think about it

misty1212 · Answer

do you see how i distributed the $-2$ on the left hand side of the inequality?

anonymous · Answer

I think so. Did you multiply 9x2?

misty1212 · Answer

actually $-2\times 9$

anonymous · Answer

Okay I'm starting to slowly get it now.

misty1212 · Answer

now comes the tricky part

anonymous · Answer

I think it's always true because the last equation is.. true... am i getting this right?

misty1212 · Answer

$$-4x-18>-4x+9$$ $x$ is a variable, so it can be anything 
but whatever it is on the left, it is the same thing on the right
so the $-4x$ on the left is equal to the $-4x$ on the right

misty1212 · Answer

adding $4x$ to both sides gives 
$$-18>9$$ which is NEVER  true

anonymous · Answer

okay okay I'm starting to understand this. I think i got it now. Thank you so much :)

misty1212 · Answer

$$\color\magenta\heartsuit$$