Question

|5x-4|=8 | - это модуль

Answer 1

|5x-4|=8

5x-4=8 или 5x-4=-8

5x=8+4 5x=-8+4

5x=12 5x=-4

x=2,4 x=-0,8

Answer 2

|5х-4|=8
5х-4=8 или 5х-4=-8
х=12/5 или х=-4/5

Answer 3

To solve the equation |5x-4| = 8, we need to consider two cases:

Case 1: 5x-4 is positive, i.e., 5x-4 > 0

In this case, we have |5x-4| = 5x-4, so we can write:

5x-4 = 8

Adding 4 to both sides, we get:

5x = 12

Dividing both sides by 5, we get:

x = 12/5

So, in this case, the solution is x = 12/5.

Case 2: 5x-4 is negative, i.e., 5x-4 < 0

In this case, we have |5x-4| = -(5x-4), so we can write:

-(5x-4) = 8

Simplifying, we get:

-5x + 4 = 8

Subtracting 4 from both sides, we get:

-5x = 4

Dividing both sides by -5 (and remembering that dividing an inequality by a negative number flips the inequality sign), we get:

x < -4/5

So, in this case, the solution is x < -4/5.

Therefore, the solutions to the equation |5x-4| = 8 are x = 12/5 or x < -4/5.