Question

|2x+1|=3 and |3x -2|=7

Answer 1

1) либо 2х+1 = 3
х = 1
либо 2х +1 = -3
х =-2
2) либо 3х-2 = 7
х = 3
либо 3х-2=-7
х = -5/3

Answer 2

To solve the system of absolute value equations:

1. |2x + 1| = 3
2. |3x - 2| = 7

We need to consider both the positive and negative cases for each absolute value equation.

Solving |2x + 1| = 3:

Positive case: 2x + 1 = 3 2x = 3 - 1 2x = 2 x = 1

Negative case: -(2x + 1) = 3 -2x - 1 = 3 -2x = 3 + 1 -2x = 4 x = -2

So, for the first equation, the solutions are x = 1 and x = -2.

Solving |3x - 2| = 7:

Positive case: 3x - 2 = 7 3x = 7 + 2 3x = 9 x = 3

Negative case: -(3x - 2) = 7 -3x + 2 = 7 -3x = 7 - 2 -3x = 5 x = -5/3

So, for the second equation, the solutions are x = 3 and x = -5/3.

Therefore, the combined solution for the system of equations is x = -2, x = -5/3, x = 1, and x = 3.