Question

The solution set of the equation |x - 1| = 3 is _____
{-2, 4}
{-3, 3}
{-4, 2}

Answer 1

Answer: The correct option is

(A) {-2, 7}.

Step-by-step explanation: We are given to find the solution set of the following :

`|x-1|=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the following property of modulus :

`|y|=b~~\Rightarrow y=b~or~y=-b.`

So, from (i), we get

`|x-1|=3\\\\\Rightarrow x-1=3~~or~~x-1=-3\\\\\Rightarrow x=3+1~~~~\Rightarrow x=-3+1\\\\\Rightarrow x=4,-2.`

Thus, the required solution set is {-2, 4}.

Option (A) is CORRECT.

Answer 2

{-2, 4}

Explanation:

|x - 1| = 3

There are two cases, one positive and one negative

x - 1 = 3 and x-1 = -3

Add 1 to each side

x-1+1 = 3+1 x-1+1 = -3+1

x =4 x = -2