What is the solution set for |2x – 3| = 11?

You have two possibilities.

2x - 3 = 11 or -(2x - 3) = 11

2x - 3 = 11

2x = 14

x = 7

-(2x - 3) = 11

-2x + 3 = 11

-2x = 8

x = -4

x = -4 or x = 7

|2x – 3| = 11

2x - 3 can be 11 or - 11

2x - 3 = 11

2x = 14

x = 7

2x - 3 = - 11

2x = - 8

x = - 4

2x - 3 = 11 or 2x - 3 = - 11

First we solve 2x - 3 = 11

=> 2x = 11 + 3

= x = 14/2

= [ x = 7 ] -------------------- (1)

Now solve 2x - 3 = - 11

2x = - 11 + 3

x = - 8/2

[ x = - 4 ] ------------------ (2)

By 1 & 2 the solution set is (7, - 4)

|2x-3| = 11

2x - 3 = 11, 2x - 3 = -11

x = 7, x = -4

|2x-3|=11

2x-3=11

2x=14

x=7

-----------

-(2x-3)=11

-2x+3=11

2x=-8

x=-4

x=7 and x=-4 are the solutions

7 and - 4

|2*7 -3| = 11

|2* (-4) - 3| = 11

A slightly different way is to eliminate thhe absolute function by squaring hence:

(2x - 3)^2 = 121

4x^2 - 12x - 112 = 0

x^2 - 3x - 28 = 0

(x - 7)(x + 4) = 0

x = 7 or x = -4

-4 and 7

|2x-3|=11<=>

2x-3=11 or 2x-3=-11<=>

x=7 or -4

S.S={-4,7}

7 & 4