Question

Помогите! решите пожалуйста подробно, заранее спасибо. 1) I x-2 I = 3,4 2) I 3-x I = 5,1 3) I 2x+1 I =5 4) I 1-2x I = 7 5) I 3x+2 I = 5 6) I 7x-3 I =3

Answer 1

Решение смотри на фотографии

Answer 2

1) I|x-2| = 3.4

To solve this equation, we need to consider two cases - one where the expression inside the absolute value is positive and one where it is negative.

Case 1: x - 2 > 0 In this case, the absolute value simplifies to Ix - 2I = 3.4. We can rewrite this equation as two separate equations: 1) x - 2 = 3.4 2) x - 2 = -3.4

Solving equation 1, we get: x = 3.4 + 2 x = 5.4

Solving equation 2, we get: x = -3.4 + 2 x = -1.4

Case 2: x - 2 < 0 In this case, the absolute value simplifies to I-(x - 2)I = 3.4. We can rewrite this equation as two separate equations: 1) -(x - 2) = 3.4 2) -(x - 2) = -3.4

Solving equation 1, we get: -x + 2 = 3.4 -x = 3.4 - 2 -x = 1.4 x = -1.4 (We reject this solution because it does not satisfy the condition x - 2 < 0)

Solving equation 2, we get: -(x - 2) = -3.4 x - 2 = 3.4 x = 3.4 + 2 x = 5.4

Therefore, the solutions to the equation I|x - 2| = 3.4 are x = -1.4 and x = 5.4.

2) I3 - xI = 5.1

Similar to the previous equation, we need to consider two cases - one where 3 - x > 0 and one where 3 - x < 0.

Case 1: 3 - x > 0 In this case, the absolute value simplifies to I3 - xI = 5.1. We can rewrite this equation as two separate equations: 1) 3 - x = 5.1 2) 3 - x = -5.1

Solving equation 1, we get: -x = 5.1 - 3 -x = 2.1 x = -2.1

Solving equation 2, we get: -x = -5.1 - 3 -x = -8.1 x = 8.1 (We reject this solution because it does not satisfy the condition 3 - x > 0)

Case 2: 3 - x < 0 In this case, the absolute value simplifies to I-(3 - x)I = 5.1. We can rewrite this equation as two separate equations: 1) -(3 - x) = 5.1 2) -(3 - x) = -5.1

Solving equation 1, we get: x - 3 = 5.1 x = 5.1 + 3 x = 8.1 (We reject this solution because it does not satisfy the condition 3 - x < 0)

Solving equation 2, we get: -(3 - x) = -5.1 -x + 3 = -5.1 -x = -5.1 - 3 -x = -8.1 x = 8.1

Therefore, the solution to the equation I3 - xI = 5.1 is x = -2.1.

3) I2x + 1I = 5

To solve this equation, we need to consider two cases - one where 2x + 1 > 0 and one where 2x + 1 < 0.

Case 1: 2x + 1 > 0 In this case, the absolute value simplifies to I2x + 1I = 5. We can rewrite this equation as two separate equations: 1) 2x + 1 = 5 2) 2x + 1 = -5

Solving equation 1, we get: 2x = 5 - 1 2x = 4 x = 4/2 x = 2

Solving equation 2, we get: 2x = -5 - 1 2x = -6 x = -6/2 x = -3

Case 2: 2x + 1 < 0 In this case, the absolute value simplifies to I-(2x + 1)I = 5. We can rewrite this equation as two separate equations: 1) -(2x + 1) = 5 2) -(2x + 1) = -5

Solving equation 1, we get: -2x - 1 = 5 -2x = 5 + 1 -2x = 6 x = 6/-2 x = -3

Solving equation 2, we get: -2x - 1 = -5 -2x = -5 - 1 -2x = -6 x = -6/-2 x = 3

Therefore, the solutions to the equation I2x + 1I = 5 are x = -3 and x = 2.

4) I1 - 2xI = 7

Similar to the previous equation, we need to consider two cases - one where 1 - 2x > 0 and one where 1 - 2x < 0.

Case 1: 1 - 2x > 0 In this case, the absolute value simplifies to I1 - 2xI = 7. We can rewrite this equation as two separate equations: 1) 1 - 2x = 7 2) 1 - 2x = -7

Solving equation 1, we get: -2x = 7 - 1 -2x = 6 x = 6/-2 x = -3

Solving equation 2, we get: -2x = -7 - 1 -2x = -8 x = -8/-2 x = 4

Case 2: 1 - 2x < 0 In this case, the absolute value simplifies to I-(1 - 2x)I = 7. We can rewrite this equation as two separate equations: 1) -(1 - 2x) = 7 2) -(1 - 2x) = -7

Solving equation 1, we get: 2x - 1 = 7 2x = 7 + 1 2x = 8 x = 8/2 x = 4

Solving equation 2, we get: 2x - 1 = -7 2x = -7 + 1 2x = -6 x = -6/2 x = -3

Therefore, the solutions to the equation I1 - 2xI = 7 are x = -3 and x = 4.

5) I3x + 2I = 5

To solve this equation, we need to consider two cases - one where 3x + 2 > 0 and one where 3x + 2 < 0.

Case 1: 3x + 2 > 0 In this case, the absolute value simplifies to I3x + 2I = 5. We can rewrite this equation as two separate equations: 1) 3x + 2 = 5 2) 3x + 2 = -5

Solving equation 1, we get: 3x = 5 - 2 3x = 3 x = 3/3 x = 1

Solving equation 2, we get: 3x = -5 - 2 3x = -7 x = -7/3

Case 2: 3x + 2 < 0 In this case, the absolute value simplifies to I-(3x + 2)I = 5. We can rewrite this equation as two separate equations: 1) -(3x + 2) = 5 2) -(3x + 2) = -5

Solving equation 1, we get: -3x - 2 = 5 -3x = 5 + 2 -3x = 7 x = 7/-3

Solving equation 2, we get: -3x - 2 = -5 -3x = -5 + 2 -3x = -3 x = -3/-3 x = 1

Therefore, the solutions to the equation I3x + 2I = 5 are x = -7/3 and x = 1.

6) I7x - 3I = 3

To solve this equation, we need to consider two cases - one where 7x - 3 > 0 and one where 7x - 3 < 0.

Case 1: 7x - 3 > 0 In this case, the absolute value simplifies to I7x - 3I = 3. We can rewrite this equation as two separate equations: 1) 7x - 3 = 3 2)