Question

solve the following equations |x-3|+|x+2|-|x-4|=3​

Answer 1

Step-by-step explanation:

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

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

x+3=3

x=3-3

x=0

Answer 2

Answer:

To solve this problem we need to consider different range of ‘x',

For x < -2

Equation will be

-(x-3)-(x+2)+(x-4)=3

-x+3–2–4=3

x=-6———-(1) for x < -2

For -2 <x<3

-(x-3)+(x+2)+(x-4)=3

x+3+2–4=3

x=2 —————-(2) For -2 <x<3

For 3<x<4

(x-3)+(x+2)+(x-4)=3

3x+2–7=3

x=8/3 =2.6666 ————-(3) For 3<x<4

For x>4

(x-3)+(x+2)-(x-4)=3

x=0 ————-(4) For x>4

From equation (1) to (4)

We can see that value of x=-6 and x=2 only satisfied its range, hence these two value of x are solution.