Question

Помогите решить уравнения:2х - 1.8 ( х - 3) = - 3.24 - 0.5 ( х + 9 ) = - 2.12 ( х - 4) - 1.2 ( х + 7 ) = - 0.43 ( х + 1) - 2.4 ( х - 0.5) = - 0.60.2 * (3|x| - 5) - 3 * ( 0.4 - 0.3 |x| ) = - 0.71.1 * ( 2|x| - 3) - 2 * ( 0.8 + |x| ) = - 0.9

Answer 1

2x-1,8x+5,4=-3,2

0,2x=-2,2

x=-11

 

4-0,5x-4,5=-2,1

-0,5x=1,6

 

2x-8-1,2x-8,4=-0,4

0,8x=16,8

x=21

Answer 2

2х - 1,8 (х-3)= -3,2

2х - 1,8х + 5,4 + 3,2=0

0,2х + 8,6=0

0,2х = -8,6

х= -43

 

4 - 0.5 ( х + 9 ) = - 2.1

4 - 0,5х - 4,5 + 2,1=0

-0,5х + 1,6=0

-0,5х= -1,6

х=3,2

 

2 ( х - 4) - 1.2 ( х + 7 ) = - 0.4

2х - 8 - 1,2х - 8,4 + 0,4=0

0,8х - 16=0

0,8х=16

х=20

 

3 ( х + 1) - 2.4 ( х - 0.5) = - 0.6

3х + 3 - 2,4х + 1,2 + 0,6=0

0,6х + 4,8=0

0,6х= -48

х= -8

 

Answer 3

To solve these equations, we'll simplify each equation by combining like terms and then isolate the variable on one side of the equation. Let's go through each equation step by step:

Equation 1: 2x - 1.8 + (x - 3) = -3.24 - 0.5 + (x + 9)

Simplifying the equation: 2x + x - 1.8 - 3 = -3.24 - 0.5 + x + 9 3x - 4.8 = x + 5.26

Isolating the variable: 3x - x = 5.26 + 4.8 2x = 10.06 x = 10.06 / 2 x = 5.03

So, the solution to Equation 1 is x = 5.03.

Equation 2: -2.12 + (x - 4) - 1.2 + (x + 7) = -0.43 + (x + 1) - 2.4 + (x - 0.5)

Simplifying the equation: x - 4 + x + 7 - 2.12 - 1.2 = x + 1 - 0.43 - 2.4 + x - 0.5 2x + 3.68 = 2x - 1.33

After simplifying, we can see that both sides of the equation have 2x terms, which means the equation has no unique solution. The equation is inconsistent.

Equation 3: 0.2 * (3|x| - 5) - 3 * (0.4 - 0.3|x|) = -0.71

To solve this equation, we need to consider two cases: one where x is positive and one where x is negative.

Case 1: x is positive (x > 0) 0.2 * (3x - 5) - 3 * (0.4 - 0.3x) = -0.71

Simplifying the equation: 0.6x - 1 - 0.12 + 0.09x = -0.71 0.69x - 1.12 = -0.71

Isolating the variable: 0.69x = -0.71 + 1.12 0.69x = 0.41 x = 0.41 / 0.69 x ≈ 0.594

Case 2: x is negative (x < 0) 0.2 * (3(-x) - 5) - 3 * (0.4 - 0.3(-x)) = -0.71

Simplifying the equation: -0.6x - 1 - 0.12 + 0.09x = -0.71 -0.51x - 1.12 = -0.71

Isolating the variable: -0.51x = -0.71 + 1.12 -0.51x = 0.41 x = 0.41 / -0.51 x ≈ -0.804

So, the solutions to Equation 3 are x ≈ 0.594 and x ≈ -0.804.

Equation 4: 1.1 * (2|x| - 3) - 2 * (0.8 + |x|) = -0.9

To solve this equation, we'll consider two cases as well.

Case 1: x is positive (x > 0) 1.1 * (2x - 3) - 2 * (0.8 + x) = -0.9

Simplifying the equation: 2.2x - 3.3 - 1.6 - 2x = -0.9 0.2x - 4.9 = -0.9

Isolating the variable: 0.2x = -0.9 + 4.9 0.2x = 4 x = 4 / 0.2 x = 20

Case 2: x is negative (x < 0) 1.1 * (2(-