Paper 1 · modulus / inequalities

Given that $-4 < x < 2$ is the solution of the inequality $|x + a| < b$ , find the values of $a$ and $b$ .

a = -1

b = 3

a = 3

b = 1

a = 1

b = 3

a = 1

b = 6

Explanation:

|x+a|<b

means

-b-a<x<b-a

. Matching with

-4<x<2

-b-a=-4

and

b-a=2

. Adding gives

-2a=-2

, so

a=1

and

b=3

Derived from ZIMSEC Mathematics Paper 1, June 2012, Q1

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