Question

Solve |3x+2| - |x-3| = 1​

Answer 1

Step-by-step explanation:

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

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

|2x+5|=1

|2x|= -4

|x| = -2

x = 2

Answer 2

Step-by-step explanation:

Given :-

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

To find :-

Solve the given equation ?

Solution :-

Given equation is |3x+2| - |x-3| = 1

We know that

|x| = x if x>0 or |x| = -x, if x< 0

|x| = x and |-x| = x

Now ,We have ,

(3x+2)-(x-3) = 1 or -[(3x+2)-(x-3)] = 1

Case -1:-

(3x+2)-(x-3) = 1

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

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

=> 2x+5 = 1

=> 2x = 1-5

=> 2x = -4

=> x = -4/2

=> x = -2

and

-[(3x+2)-(x-3)]= 1

=> -[3x+2-x+3] = 1

=> -[3x-x+2+3] = 1

=> -[2x+5] = 1

=> -2x-5= 1

=> -2x = 1+5

=> -2x = 6

=> x = 6/-2

=> x = -3

=> x = -3

Therefore, x = -2 or -3

Answer:-

The value of x = -2 or -3

Check :-

If x = -2 then LHS of the given equation

=>[3(-2)+2 ] -(-2-3)

=>( -6+2)-(-5)

=> (-4)+5

=> 1

=> RHS

LHS = RHS is true for x = -2

and

If x = -3 then LHS of the given equation

=> =>-[3(-3)+2 ] -(-3-3)]

=>-[( -9+2)-(-6)]

=> -[(-7)+6]

=> -(-1)

=> 1

=> RHS

LHS = RHS is true for x = -3

Verified the given relations in the given problem.

Used formulae:-

→ |x| = x

→ |-x| = x