Question

1). 11-2(4x-y) 2). 2(a-6) (a+6)-(a+7) 3). -(x-y)+(x-1) (y+1) Решить уравнение: 3(5x+2)-6=2x+11 4x-15=11-2(4x-1)

Answer 1

3(5х +2) -6 = 2х+11
15х +6 - 6= 2х+11
15х -2х=11
13х= 11
х= 11/13

4х-15= 11-2(4х-1)
4х-15=11-8х+2
4х+8х=2+11+15
12х= 28
х= 28/12
х= 7/3. 

1) 11-2(4х-у)
11-8х+2у 
2у=8х-11
(таблицу)

2) 2(а-6)(а+6)-(а+7)= (2а-12)(а+6)-(а+7)= 2a²+12a-12a-72-a-7=2a²-72.
2а²-72=0
2a² =72
a² =36
a1 =6
a2 =-6.

3) -(x-y)+(x-1)(y+1)= -x+y+xy+x-y-1= xy-1.

Answer 2

To solve the given equations, let's solve them one by one:

1. 11 - 2(4x - y)

To simplify the expression, distribute the -2:

= 11 - 8x + 2y

2. 2(a - 6)(a + 6) - (a + 7)(a + 6)

To simplify the expression, distribute the 2 and the negative sign:

= 2(a^2 + 6a - 6a - 36) - (a^2 + 6a + 7a + 42)

Combine like terms:

= 2(a^2 - 36) - (a^2 + 13a + 42)

Now distribute the negative sign:

= 2a^2 - 72 - a^2 - 13a - 42

Combine like terms again:

= a^2 - 13a - 114

3. -(x - y) + (x - 1)(y + 1)

To simplify the expression, distribute the negative sign and the (x - 1):

= -x + y + xy + x - 1

Combine like terms:

= xy + y - x - 1

4. To solve the equation: 3(5x + 2) - 6 = 2x + 11

Step 1: Distribute the 3 on the left side:

15x + 6 - 6 = 2x + 11

Step 2: Combine like terms:

15x = 2x + 11

Step 3: Move all the x terms to one side by subtracting 2x from both sides:

15x - 2x = 2x - 2x + 11

13x = 11

Step 4: Finally, isolate x by dividing both sides by 13:

x = 11 / 13

So the solution to the equation is x = 11/13.

5. To solve the equation: 4x - 15 = 11 - 2(4x - 1)

Step 1: Distribute the -2 on the right side:

4x - 15 = 11 - 8x + 2

Step 2: Combine like terms:

4x - 15 = -8x + 13

Step 3: Move all the x terms to one side by adding 8x to both sides:

4x + 8x - 15 = -8x + 8x + 13

12x - 15 = 13

Step 4: Now, isolate x by adding 15 to both sides:

12x - 15 + 15 = 13 + 15

12x = 28

Step 5: Finally, divide both sides by 12 to get the value of x:

x = 28 / 12 x = 7/3

So the solution to the equation is x = 7/3.

Please double-check all the solutions and steps for accuracy, as manual calculations can have errors.