Which graph shows the solution of the inequality? Please Help I'll Give Medal!!!

Question

anonymous · Answer

|dw:1397090924130:dw|

anonymous · Answer

Take your time

ranga · Answer

$$-\frac{x}{2} \le 8$$To solve for x multiply both sides by 2:$$-x \le 16$$

anonymous · Answer

ok
yeah thats what i got but i don't know how to do the thing on the number line to get my answer

anonymous · Answer

But i understand that part

ranga · Answer

Multiply both sides by -1.  When you multiply by a negative sign you have to flip the "less than or equal to"  to  "greater than or equal to".
$$ x \ge -16$$

anonymous · Answer

i thought i multiply by 2 ?

ranga · Answer

So on a number line, mark the -16 and anything to the right of it including -16 is a solution.

anonymous · Answer

Not 1?

ranga · Answer

I multiplied by 2 and got  -x <= 16
but I want to solve for x and not minus x.  So multiply both sides by -1.
x >= -16 is the solution.

ranga · Answer

When you multiply by a negative number the inequality will flip.

anonymous · Answer

so your still going to get the same answer?

ranga · Answer

same as what?  
The steps I told you is the way to get the correct answer.

anonymous · Answer

Ohhh the sign will flip the > and <

anonymous · Answer

Correct?

ranga · Answer

Yes, multiplying by a NEGATIVE number will flip > to < or < to > or <= to >= or >= to <=

ranga · Answer

Here we have <= and so multiplying or dividing by a negative number will flip the inequality to >=

anonymous · Answer

ok

ranga · Answer

Oh, it lost my drawing. :(

ranga · Answer

But the solution is x in the interval [-16, infinity)
In a number line mark the point -16 and draw a horizontal line from -16 to the positive x side and put an arrow.  Make sure that point -16 is included in the solution because we have x >= -16.