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.

step-by-step explanation: