Question

1) 5у-(7-2у)-(4у+8)=2у 2) 6у(13у-9)-13у(6у-1)=24+13 3) (2х-3)² -(2х+1)(2х-5)=3х-14

Answer 1

5y  - ( 7 - 2y) - (7y + 8) = 2y
5y  - 7  + 2y   - 7y  - 8  = 2y
(5y  + 2y  - 7y)  - (7 + 8) = 2y 
- 15  =  2y
2y = - 15
y =  - 15/2
y =  - 7,5

6у(13у-9)  - 13у(6у - 1) = 24 +13
78у²   - 54у  -  78у²  + 13у = 37
(78у² - 78у² ) - (54у-13у) = 37
-41у = 37
у= - ³⁷/₄₁

(2х   - 3)² - (2х + 1)(2х - 5) = 3х - 14
(2х)²  - 2*2х * 3  +  3²  - (4х² - 10х  + 2х  - 5) = 3х  - 14
4х²  - 12х  + 9  - (4х²  - 8х  - 5)   =  3х  - 14
4х²  - 12х  + 9  - 4х²  + 8х  + 5   =  3х  - 14
(4х²  - 4х²)   - (12х - 8х)  + (9 + 5) = 3х  - 14
- 4х  + 14  =  3х  - 14
- 4х   - 3х  = - 14 - 14
- 7х =  - 28
7х = 28
х = 28 : 7
х = 4

Answer 2

Let's solve each of the given equations step by step:

1. $5у - (7 - 2у) - (4у + 8) = 2у$

Step 1: Remove the parentheses: $5у - 7 + 2у - 4у - 8 = 2у$

Step 2: Combine like terms on the left side: $3у - 15 = 2у$

Step 3: Move all terms containing "у" to one side of the equation: $3у - 2у = 15$

Step 4: Simplify the equation: $у = 15$

So, the solution to the equation is $у = 15$.

2. $6у(13у - 9) - 13у(6у - 1) = 24 + 13$

Step 1: Use the distributive property to remove the parentheses: $78у^2 - 54у - 78у^2 + 13у = 37$

Step 2: Combine like terms on the left side: $-41у = 37$

Step 3: Solve for "у" by dividing both sides by -41: $у = -\frac{37}{41}$

So, the solution to the equation is $у = -\frac{37}{41}$.

3. $(2х - 3)² - (2х + 1)(2х - 5) = 3х - 14$

Step 1: Expand $(2х - 3)²$: $4х² - 12х + 9 - (2х + 1)(2х - 5) = 3х - 14$

Step 2: Use the distributive property to remove the parentheses: $4х² - 12х + 9 - (4х² - 10х - 2х + 5) = 3х - 14$

Step 3: Combine like terms on the left side: $4х² - 12х + 9 - 4х² + 12х - 5 = 3х - 14$

Step 4: Simplify the equation: $4х - 4 = 3х - 14$

Step 5: Move all terms containing "х" to one side of the equation: $4х - 3х = -14 + 4$

Step 6: Simplify the equation: $х = -10$

So, the solution to the equation is $х = -10$.

Please double-check the solutions to ensure they are correct. If you have any further questions or need additional assistance, feel free to ask!