Question

|3х+2|=|x-1| |x-5|=|x+1|

Answer 1

Ответ:

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Answer 2

To solve the given system of equations:

|3x + 2| = |x - 1| |x - 5| = |x + 1|

Let's consider each equation separately.

For the first equation, |3x + 2| = |x - 1|, we have two cases to consider:

Case 1: (3x + 2) = (x - 1) Solving this equation, we get: 3x + 2 = x - 1 2x = -3 x = -3/2

Case 2: -(3x + 2) = (x - 1) Solving this equation, we get: -3x - 2 = x - 1 -4x = 1 x = -1/4

So, for the first equation, we have two solutions: x = -3/2 and x = -1/4.

Now, let's move on to the second equation, |x - 5| = |x + 1|.

Case 1: (x - 5) = (x + 1) Solving this equation, we get: x - 5 = x + 1 -5 = 1

Since this equation has no solution, we move on to the next case.

Case 2: -(x - 5) = (x + 1) Solving this equation, we get:

• x + 5 = x + 1 10 = 2x x = 5

So, for the second equation, we have one solution: x = 5.

In conclusion, the solutions to the system of equations are: x = -3/2, x = -1/4, and x = 5.