Solve: | 1 - 0.3 x | ≥ -3

Question

Solve;

|

0.25

y

+

5

|

>

-0.75

solve:

7

-

|

3

y

-

2

|

≤

1

solve:

|

4

+

2

y

|

≥

-3

solve:

|

1

-

0.3

x

|

≥

-3

 

Answer 1

|1-0.3x|≥-3 is true for all x because all absolute values are positive, and all positive numbers are greater than all negative numbers. The same applies to y in |0.25y+5|>-0.75 and |4+2y|≥-3.

7-|3y-2|≤1 is the same as 6≤|3y-2| or |3y-2|≥6. 

3y-2≥6, 3y≥8, y≥8/3; 2-3y≥6, -4≥3y, -4/3≥y, y≤-4/3. So y≥8/3 or y≤-4/3 is the solution.