Question

Решите уравнения: I 2x-5 I=3; I 2x - 1 I=0; I 5x - 2 I=-7.

Answer 1

1) 2х+5=3
2х=3-5
2х=-2
х=-2/2
х=-1
2) 2х+1=0
2х=-1
х=-1/2
3) 5х+2=-7
5х=-9
х=-9/5
х= -1,8
Если что спрашивай)

Answer 2

To solve absolute value equations like these, we need to consider both the positive and negative cases of the absolute value expression and then find the solutions for each case.

1. |2x - 5| = 3: We have two cases: a) 2x - 5 = 3: Solve for x: 2x = 3 + 5 2x = 8 x = 8 / 2 x = 4

b) -(2x - 5) = 3: Solve for x: -2x + 5 = 3 -2x = 3 - 5 -2x = -2 x = -2 / -2 x = 1

So the solutions for the equation |2x - 5| = 3 are x = 4 and x = 1.

2. |2x - 1| = 0: We have two cases: a) 2x - 1 = 0: Solve for x: 2x = 1 x = 1 / 2 x = 0.5

b) -(2x - 1) = 0: Solve for x: -2x + 1 = 0 -2x = -1 x = -1 / -2 x = 1/2 x = 0.5

Both cases result in the same solution, so the equation |2x - 1| = 0 has a single solution x = 0.5.

3. |5x - 2| = -7: The absolute value of an expression can't be negative, so there are no real solutions to this equation. If there's an absolute value on the left side of the equation and a negative number on the right side, there are no real solutions.

Therefore, the solutions to the equations are: |2x - 5| = 3 => x = 4, x = 1 |2x - 1| = 0 => x = 0.5 |5x - 2| = -7 => No real solutions.