How do i solve this do we use the multiple choice

  (C)  4|5 -2x| > 68

Step-by-step explanation:

You can solve each of the inequalities to see if their solutions match the given numbers, or you can start with the given numbers and see what sort of inequality you end up with.

If you plot the given "solution" on a number line, you find that the numbers -6 and 11 are the same distance from x=2.5. That distance is 8.5 units. (One way to deterimine this is to average -6 and 11, then subtract that average from 11 to find the distance.

So, we can write an inequality describing values of x that are more than 8.5 units from 2.5:

  |x -2.5| > 8.5

and it will have the solution x < -6 or x > 11.

Multiplying this by 2, it can become ...

   |2x -5| > 17

Of course, since the absolute value function doesn't care whether its argument is positive or negative, we can also write this as ...

   |5 -2x| > 17

This tells you right away which answer choice is appropriate. Further confirmation can be had by multiplying this by 4:

  4|5 -2x| > 68 . . . . . . matches selection C

2500

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.