Help with solving inequalities EASY 10 PONITS?

Question

Show how you got it and graph?

1. -2 ≤ -3(m+3) ≤ 3 (I got -7/3≥m≥-4 but this is an "and" problem so how would you draw the number line?)

2. p+6 ≥ |p+6|
3. 1/2a-1/8>3/4+6/5a

Thank you in advance these are the only ones left on my homework that I don't understand.

Answer 1

Given that

Add 9 on each side.

Divide each side by -3.

If we multiply a number with negative sign we have to change their sign.

Graph-;

1)Represents the obtained numbers in a number line system.

Answer 2

1) The inequality -2 ≤ -3(m + 3) ≤ 3

-2 ≤ - 3m - 9 ≤ 3

-2 + 9 ≤ -3m + 9 ≤ 3 + 9

7 ≤ - 3m ≤ 12

Multiple by each term of inequality by negitive 3 and flip the symbol.

-7/3 ≥ m  ≥ -4.

Solution -7/3 ≥ m  ≥ -4.

Graph

2) The absolute inequality  p  + 6 ≥ |p + 6|

p  + 6 ≥ p  +6

6 ≥ 6

p  + 6 ≥ - (p  + 6)

p  + 6 ≥ - p  - 6

2p ≥ -12

Solution p ≥ -6.

3) The inequality

Solution .