What are the values of a and b.if any,where a|b-2|<0?

Question

please some sugestions

Answer 1

a[b-2]< 0,
A positive number and a negative number of equal magnitude has equal absolute values. Therefore, we must solve 2 Eqs:

Eq1: a(b-2)< 0.

Eq2: a(-b+2) < 0.

a(b-2) < 0,
Divide both sides by a:
b-2 < 0,
b < 2.

Answer 2

a[b-2]< 0,
A positive number and a negative number of equal magnitude has equal absolute values. Therefore, we must solve 2 Eqs:

Eq1: a(b-2)< 0.

Eq2: a(-b+2) < 0.

Eq1: a(b-2) < 0,
Divide both sides by a:
b-2 < 0,
b < 2.
Divide both sides by (b-2):
a < 0.

Solution Set: b < 2, and a < 0.

Eq2: a(-b+2) < 0.
Divide both sides by a:
-b + 2 < 0,
-b < -2,
b > 2.

Divide both sides by (-b+2):
a < 0.

Solution set: b > 2, and a < 0.