MathCastle
Grade 6SuperchallengeAbsolute Value

Absolute Value · Superchallenge problem

The numbers aa and bb satisfy a<0<ba<0<b and ∣a∣>∣b∣|a|>|b|. How many of these six expressions are always positive?

a+b,b−a,∣a∣−b,∣a+b∣,a−∣b∣,∣a∣+aa+b,\qquad b-a,\qquad |a|-b,\qquad |a+b|,\qquad a-|b|,\qquad |a|+a