2. solve the inequality for x. show each step of the solution. 16x > 12(2x – 6) – 24

Remark

The first thing you should do is to get a program to give you a graph. I use Desmos. We'll talk about the solution shown by the graph when we are done with the solution

Solution

Remove the brackets on the right

16x > 12*2x - 12*6 - 24

16x > 24x - 72 - 24             Combine like terms

16x > 24x - 96                    Add 96 to both sides.

16x + 96 > 24x                   Subtract 16x from both sides.

96 >  24x - 16x                  

96 > 8x                               Divide 8

96/8 > x

12 > x

Graph

Now we can discuss the graph. The dotted broken line which separates the white from the pink is x = 12. That's the boundary to this inequality. The line itself is parallel to the y axis. Everything to the left of x = 12 is a possible solution to the inequality if it is a number on the x axis. What to do with the y values is an answer for another day.   There are many solutions to this inequality, unlike an equation which has only one at the level of your current math class.

42

step-by-step explanation:

256/6=42

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.