Question

(х-4,5)/2=(-2х-3,5)/3 -2(х+5)+1=-3(х+1) |х|-15=9-5|х|.

Answer 1

1) (x - 4,5)/2 = (-2x - 3,5)/3
     3*(x - 4,5) = 2*(-2x - 3,5)
     3x - 13,5 = -4x - 7
     7x = 6,5
       x = 13/14

Ответ: {13/14}

2) -2(x + 5) + 1 = -3(x + 1)
    -2x - 10 + 1 = -3x - 3
     x = 9 - 3
     x = 6

Ответ: {6}

3) |x| - 15 = 9 - 5|x|
    6|x| = 24
    |x| = 4
    x = 4
    x = -4

Ответ: {-4; 4}

Answer 2

To solve these equations, we can follow these steps:

1. Simplify both sides of the equation by distributing any constants and combining like terms.
2. Move all the variables to one side of the equation and all the constants to the other side.
3. If there are absolute values involved, consider both the positive and negative cases for the expression inside the absolute value bars.

Let's solve each equation:

1. (х-4,5)/2=(-2х-3,5)/3

First, we can simplify the equation by cross-multiplying to get rid of the fractions:

3(х-4.5) = 2(-2х-3.5)

Simplifying further:

3х - 13.5 = -4х - 7

Bringing all the variables to one side and all the constants to the other side:

3х + 4х = -7 + 13.5

7х = 6.5

х = 0.92857 (rounded to 5 decimal places)

Therefore, the solution to the equation is х = 0.92857.

2. -2(х+5)+1=-3(х+1)

First, we can simplify the equation by distributing the constants:

-2х - 10 + 1 = -3х - 3

Simplifying further:

-2х - 9 = -3х - 3

Bringing all the variables to one side and all the constants to the other side:

-2х + 3х = -3 + 9

х = 6

Therefore, the solution to the equation is х = 6.

3. |х|-15=9-5|х|

We can split this equation into two cases: one where х is positive or zero, and one where х is negative.

Case 1: х ≥ 0

In this case, the absolute value is equal to х, so we can simplify the equation:

х - 15 = 9 - 5х

Bringing all the variables to one side and all the constants to the other side:

6х = 24

х = 4

Therefore, in this case, the solution to the equation is х = 4.

Case 2: х < 0

In this case, the absolute value is equal to -х, so we can simplify the equation:

-х - 15 = 9 + 5х

Bringing all the variables to one side and all the constants to the other side:

6х = -24

х = -4

Therefore, in this case, the solution to the equation is х = -4.

Therefore, the solutions to the equation are х = 4 or х = -4, depending on the sign of х.