Question

What is the answer to this inequality?
Please wait. . . .

Answer 1

\[-\frac{ 3 }{ 2 }\ \left( -4x +8 \right)\le -\frac{ 1 }{ 2 }x + 3\]

Answer 2

you first need to distribute through the parenthesis. Do you know how to do that ?

Answer 3

Oh yes.

Answer 4

Would it be \[\frac{ 24 }{ 2 }x + -\frac{ 48 }{ 2 } \le -\frac{ 1 }{ 2 }x \]

Answer 5

+ 3

Answer 6

no....
-3/2 (-4x + 8) <= -1/2x + 3
12/2x - 24/2 <= -1/2x + 3
if you want to get rid of the fractions, multiply the inequality by the common denominator which is 2.
leaving you with : 12x - 24 <= -1x + 6

you still with me on this ?

Answer 7

Yes I am. And oh. I understand. So how come it isn't 12/2x + (-24/2)?

Answer 8

that would be the same....12/2x + (-24/2), but remember that a positive times a negative gives you a negative, so that would equal 12/2x - 24/2
understand ?

Answer 9

Ohhhh. Yes I do understand that part. Can you help me on solving the rest of it, I'm still kinda shaky on whether to take 12x and -1x or -24 and 6.

Answer 10

12x - 24 <= -1x + 6 (we want all the x variables on one side, so lets add 1x to both sides)
12x + 1x - 24 <= -1x + 1x + 6 (combine like terms)
13x - 24 <= 6 (now we will add 24 to both sides)
13x - 24 + 24 <= 6 + 24 (combine like terms)
13x <= 30 (now divide by 13)
x <= 30/13
unless you need it in mixed number form, then it is :
x <= 2 4/13

Answer 11

I understand now! Thanks so much for you help!

Answer 12

no problem :)