Question

|х+3|-|х-4|=4|х-1|+|х+2|=4

Answer 1

Х+3-х+4=4
0х=-3
х=0
х+1+х+2=4
2х=1
х=1:2
х=0,5

Answer 2

Let's break this down into two separate equations using the definition of absolute value:

First, we have:

|х+3| - |х-4| = 4|х-1|

Notice that there are only two possible cases for the expressions inside the absolute value signs:

1. х+3 is greater than or equal to х-4, which gives us: х+3 - (х-4) = 7
2. х+3 is less than х-4, which gives us: -х-3 + (х-4) = 1

Simplifying both of these equations, we get:

1. 7 = 4|х-1|
2. -1 = 4|х-1|

For the second equation, we have:

|х+2| = 4 - |х-1|

Again, there are only two possible cases:

1. х+2 is greater than or equal to х-1, which gives us: х+2 - (х-1) = 4 - (х-1)
2. х+2 is less than х-1, which gives us: -х-2 + (х-1) = 4 - (х-1)

Simplifying both of these equations, we get:

1. 3х = 4
2. -3х = 6

However, neither of these equations have a solution that satisfies the original equation, so there are no solutions to the equation |х+3|-|х-4|=4|х-1|+|х+2|=4.