solve my compound inequality?

Question

solve my compound inequality and write the solution set in interval notation and graph it:

-3 ≤ 3 - 2x < 11

Answer 1

dump the inequalities and change them for = signs.
This gives two equations stuck together to solve :

-3 = 3 - 2x and 3 - 2x = 11

Solving these gives us 3 and -4

Giving us two lines to draw on the graph x = 3 and x=-4 remembering that this second line must be dotted cos it cannot equal it - see original inequality. Our answer is the bit between these two lines -shade it in - job done.

Answer 2

1) Break up the inequalty
-3 ≤ 3 - 2x
3 - 2x < 11

2) Treat the inequalities as =
-3 = 3 - 2x
3 - 2x = 11

3) Solve linear equations...
-3 = 3 - 2x
2x-3=3
2x=6
x=3

3 - 2x = 11
-2x=8
x=-4

4) Put back the inequalities...
x≤3
x>-4
(If you find this hard, try to put the thing in a context that makes sense, i.e. next part gives a clue)

5) Combine the 2 together...
3≥x>-4

Answer 3

-2m is between 6 and 10 so -m is between 3 and 5 so m is between -3 and -5 so -3>m>-5 and -6>2m>-10

Answer 4

the first two answers you got are both excellent