Question

Part 1: Solve |2x-9|+4 less than or equal to 7. You must show all work. Use >= and <= to represent the inequalities.

Part 2: Use complete sentences to describe the graph in words

Answer 1

Subtract 4 from both sides.

Answer 2

|2x-9| +4 <=7
let's first assume (2x-9) is greater than equal to zero, when we get the solution it'll verify if we are wrong or right
is 2x-9>=0
x>=9/2
x>=4.5
now we have
2x-9+4<=7
2x<=12
x<=6
this lies in the region of x>=4.5
taking intersection of the two ranges
we get 4.5<=x<=6
now let's assume 2x-9 <0
we get x<4.5
now modulus will open by a negative sign
|2x-9|+4<=7
-2x+9+4<=7
13-7<=2x
or 2x>=6
x>=3 and we have a pre condition x<4.5 so
intersection of these two gives 3<=x<4.5
so complete solution is x belongs to [3,4.5) U [4.5,6]
which gives x is [3,6]

Answer 3

Both sides of what?
I know you took all your time to type that, but I dont understand it.