SOlve the equation : | 2x -3 | - x - 1 = 0

math 1 !! algebraa the answer is { 4 , 2/3 } i need da steps plz !

|2x - 3| - x - 1 = 0
|2x - 3| = x + 1

Note that left side ≥ 0, so x+1 ≥ 0 ----> x ≥ -1

2x - 3 = ±(x + 1)

Case 1:

2x - 3 = x + 1
2x - x = 1 + 3
x = 4

Case 2:

2x - 3 = -x - 1
2x + x = -1 + 3
3x = 2
x = 2/3

Since both values of x are ≥ -1, then both are valid

x ∈ {4, 2/3}


Mαthmφm

| 2x -3 | - x - 1 = 0

=> | 2x -3 | = x + 1

=> 2x - 3 = x + 1 or 2x - 3 = -x - 1

x = 4 or 3x = 2

x = 4 and 2/3

abs(2*x - 3) - x - 1 = 0

a)

2*x - 3 - x - 1 = 0

x = 4

b)

- (2*x - 3) - x - 1 = 0

- 2*x + 3 - x - 1 = 0

- 3*x = - 2

x = 2/3

| 2x -3 | - x - 1 = 0
Or, x-4=0
Or, x=4
Now-2x+3-x-1=0
Or, -3x=-2
Or, x=2/3
So, the solution set is {2/3,4}