Question

|3x-5|=0 |5-2x|=0 |2-5x|=3

Answer 1

1. |3x - 5| = 0
3х - 5 = 0
3х = 5
х = 5/3 = 1 2/3

отв: 1 2/3

2. |5 - 2x| = 0
5 - 2х = 0
-2х = -5
2х = 5
х = 5/2 (= 2.5)

отв: 2.5

3. |2 - 5x| = 3
[2 - 5х = 3
[2 - 5х = -3
[х1 = -1/5 (=-0.2)
[х2 = 1

отв: -0.2; 1

Answer 2

To solve the absolute value equations, we need to find the values of x that make the expressions inside the absolute value bars equal to zero. Remember that the absolute value of a number is always non-negative, and it is equal to zero only when the number inside the absolute value is zero.

1. |3x - 5| = 0: Set the expression inside the absolute value bars equal to zero and solve for x: 3x - 5 = 0 3x = 5 x = 5/3

2. |5 - 2x| = 0: Set the expression inside the absolute value bars equal to zero and solve for x: 5 - 2x = 0 -2x = -5 x = -(-5)/2 x = 5/2

3. |2 - 5x| = 3: Since the absolute value of a number cannot be negative, we have two cases to consider:

Case 1: 2 - 5x = 3 Subtract 2 from both sides: -5x = 3 - 2 -5x = 1 x = 1/(-5) x = -1/5

Case 2: -(2 - 5x) = 3 Distribute the negative sign: -2 + 5x = 3 Add 2 to both sides: 5x = 3 + 2 5x = 5 x = 5/5 x = 1

So, the solutions to the equation |2 - 5x| = 3 are x = -1/5 and x = 1.

In summary, the solutions to the three absolute value equations are: x = 5/3, x = 5/2, x = -1/5, and x = 1.