Question

Given: x - 8 > -3.

Choose the solution set.


{x | x * R, x > -9}
{x | x * R, x > -5}
{x | x * R, x > 5}
{x | x * R, x > 14}

the * is supposed to look kind of like a backwards 3

Answer 1

What do you get when you add 8 to both sides of the inequality \(x-8>-3\)? :-)

Answer 2

x > 5

Answer 3

Very good. So which of your choices is the solution set now?

Answer 4

it'd be my third choice down, right?

Answer 5

Correct. \(\{x\mid x\in\Bbb{R},\, x>5\}\) is your solution set.

Does this make sense? :-)

Answer 6

Yeah, I'm doing an Online class and it just makes things look more difficult than they should be i guess.

Answer 7

@ChristopherToni What about this one? -----> -1/2x > 4 do i multiply 4 by -1/2

Answer 8

Just curious: Is it \(-\dfrac{1}{2}x > 4\) or \(-\dfrac{1}{2x}>4\)?

Answer 9

the first one

Answer 10

Ok, so yes, what you want to do here is not multiply everything by \(-\dfrac{1}{2}\), but instead divide everything by \(-\dfrac{1}{2}\). What do you get when you do this?

Also, if you're not comfortable dividing by a fraction, it's the same as multiplying both sides by the reciprocal of that fraction. (So, instead of dividing both sides by \(-\dfrac{1}{2}\), you could instead multiply both sides by the reciprocal \(-2\)).

Answer 11

so would it be x > -8

Answer 12

Careful! What happens to the inequality when you multiply by a negative number?

Answer 13

Flip the sign?

Answer 14

Exactly. Thus, you should get \(x<-8\) instead.

Answer 15

Okay, thanks. This was a big help.

Answer 16

No problem. Glad to be of assistance! :-)