Solve for m?

Question

|2m-7|<16

Answer 1

|2m-7|<16
1) 2m-7<16
2m<23
m<23/2
m<11.5

2) -(2m-7)<16
-2m+7<16
-2m <9
-m<9/2
m> -9/2
m> -4.5

so -9.5

Answer 2

|2m - 7| < 16

First thing you have to do is get rid of the absolute value, when you do that, you make the other side a plus or minus (because if 2m - 7 is positive or negative, the absolute value would make it positive, there are two possible solutions).
2m - 7 < +/- 16

Now, just solve for m by adding 7, then dividing by 2.
2m < 7 +/- 16
m < (7 +/- 16) / 2

Then solve for the two possible values for m: (note, when it is a - 16, the < becomes a >, because there was a multiplication of a negative number, and that reverses the sign)
m < (7 + 16) / 2
m < (23) / 2
m < 11.5

or

m > (7 - 16) / 2
m > (-9) / 2
m > -4.5

So, the solution is: - 4.5 < m < 11.5

Answer 3

Case 1.
(if 2m-7>0
m> 7/2).

2m-7 < 16
2m < 23
m <11.5

Case 2.
( if 2m-7<0
2m<7
m<7/2)

-(2m-7) > 16
-2m + 7 > 16
-2m > 9
m> (9/-2)
m> -4.5

-4.5

Answer 4

break into "cases"

a) (2m-7)<16
2m < 23
m < 23/2


b) -(2m-7)<16
-2m + 7 < 16
-9 < 2m
-9/2 < m

Answer 5

l2m-7l<116
2m-7<16 & -(2m-7)<16
2m<23 & -2m<9
m<23\2 & m>-9\2
-9\2

Answer 6

Part 1
2m - 7 < 16
2m < 23
m < 23/2

Part 2
2m - 7 > - 16
2m > - 9
m > - 9/2

Combining Part 1 and Part 2 gives:-
-9/2 < m < 23/2