ABSOLUTE VALUE INEQUALITIES

Question

1) |2z-9|≤1

2) |3f+10|≥4

3) |x-3|>0

4) |2x+1|≥-2

 

My teacher makes me work each problem twice. so please work the one written above and then flip the sign and change the last number to negative and rework

 

Ex. 1)|2z-9|≤1

THEN:|2z-9|≥-1

Answer 1

Don't use the | | when you write new inequities:

|2z-9|≤1 : 2z-9≤1 or 2z-9≥-1

|3f+10|≥4 : 3f+10≥4 or 3f+10≤-4

|x-3|>0 : x-3>0 or x-3<0

|2x+1|≥ -2 : |2x+1|≥0 : 2x+1≥0 or 2x+1≤0

Note:

When |x|≤a: write x≤a or x≥ -a

When |x|≥a: write x≥a or x≤ -a

When |x|≥0: write x≤0 or |x|≥0

and when |x|≥a and a is a negative number, the inequity is correct for all values of x.