Question

Решите уравнения сразу говорю что / (слэш slash) это модуль и так 1) /5х/-4=6 2) /х-2/+8=5

Answer 1

1)|5х|-4=6 2)|х-2|+8=5
5х=10 х-2=-3
х=2 х=-1
-5х=10 -х+2=-3
х=-2 -х=-5
х=5
вроде б так)

Answer 2

I can help you solve equations with absolute values. Here is how I would solve the equations you gave me:

1) |5x - 4| = 6

To solve this equation, we need to consider two cases: when 5x - 4 is positive and when it is negative.

Case 1: 5x - 4 > 0

In this case, we can drop the absolute value signs and solve for x:

5x - 4 = 6

5x = 10

x = 2

We need to check if this solution satisfies the original equation. We can plug in x = 2 and see if the left and right sides are equal:

|5(2) - 4| = 6

|10 - 4| = 6

|6| = 6

6 = 6

This is true, so x = 2 is a valid solution.

Case 2: 5x - 4 < 0

In this case, we need to change the sign of the expression inside the absolute value and solve for x:

-(5x - 4) = 6

-5x + 4 = 6

-5x = 2

x = -0.4

We need to check if this solution satisfies the original equation. We can plug in x = -0.4 and see if the left and right sides are equal:

|5(-0.4) - 4| = 6

|-2 - 4| = 6

|-6| = 6

6 = 6

This is true, so x = -0.4 is a valid solution.

Therefore, the equation has two solutions: x = 2 and x = -0.4.

2) |x - 2| + 8 = 5

To solve this equation, we need to isolate the absolute value term and then consider two cases: when x - 2 is positive and when it is negative.

First, we subtract 8 from both sides of the equation:

|x - 2| + 8 - 8 = 5 - 8

|x - 2| = -3

Case 1: x - 2 > 0

In this case, we can drop the absolute value signs and solve for x:

x - 2 = -3

x = -1

We need to check if this solution satisfies the original equation. We can plug in x = -1 and see if the left and right sides are equal:

|-1 - 2| + 8 = 5

| -3 | + 8 = 5

3 + 8 = 5

11 = 5

This is false, so x = -1 is not a valid solution.

Case 2: x - 2 < 0

In this case, we need to change the sign of the expression inside the absolute value and solve for x:

-(x - 2) = -3

-x + 2 = -3

-x = -5

x = 5

We need to check if this solution satisfies the original equation. We can plug in x = 5 and see if the left and right sides are equal:

|5 - 2| + 8 = 5

|3| + 8 = 5

3 + 8 = 5

11 = 5

This is false, so x = 5 is not a valid solution.

Therefore, the equation has no solutions.Ответь+подробно.+Решите+уравнения+сразу+говорю+что+/+(слэш+slash)+это+модуль+и+так+1)+/5х/-4=6+2)+/х-2/+8=5