Solve for x: inequalities

Question

Solve for x in terms of a and b. Also, a>0. 
|ax+b|≥−2

Answer 1

I. ax + b ≥ 0

 

ax + b ≥ -2

ax ≥ -b - 2

x ≥ (-b - 2) / a

 

II. ax + b < 0

 

-(ax + b) ≥ -2

ax + b ≤ 2

ax ≤ = b + 2

x ≤ (b + 2) / a

 

(-b - 2) / a ≤ x ≤ (b + 2) / a