Solve and show all work |2×+3| -6=11

x = -10; x = 7  

Step-by-step explanation:

|2x + 3| - 6 =11

Add 6 to each side.

|2x + 3| = 17

Apply the absolute rule: If |x| = a, then x = a or x = -a.

(1) 2x + 3 = 17                    (2) 2x + 3 = -17

Subtract 3 from each side

         2x = 14                                 2x = -20

Divide each side by 2

          x = 7                                   x = -10

Check:

(1) |2(7) + 3| - 6 = 11                     (2) |2(-10) + 3| - 6 = 11

      |14 + 3| - 6 = 11                              |-20 + 3| - 6 = 11

             |17| - 6 = 11                                     |-17| - 6 = 1 1

              17 - 6 = 11                                        17 - 6 = 11

                    11 = 11                                              11 = 11

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

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'.