Question

А) 3х +4 = 7х -8; б) 2 у – 3= 10; в) 2(х + 1) = 3 ( х +1); г) 3х – 5=3 +3х; д) 5у + 10 = 5( 2 + у).

Answer 1

Ответ:

Пошаговое объяснение:

а)

3х +4 = 7х -8;

7x - 3x = 4 + 8

4x = 12

x = 12 : 4

x = 3

б)

2 у – 3= 10;

2y = 10+3

2y = 13

y = 13 : 2

y = 6,5

в)

2(х + 1) = 3 ( х +1);

2x + 2 = 3x + 3

3x - 2x = 2 - 3

x = -1

г)

3х – 5=3 +3х;

3x - 3x = 3 + 5

0 ≠ 8

нет решений

д)

5у + 10 = 5( 2 + у).

5y + 10 = 10 + 5y

5y - 5y = 10 - 10

0 = 0

y є (-∞ ; ∞)

множество решений

Answer 2

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

a) 3x + 4 = 7x - 8

To solve for x, we need to isolate the variable on one side of the equation. We can start by moving the terms containing x to one side and the constant terms to the other side:

3x - 7x = -8 - 4

Simplifying:

-4x = -12

Next, we can divide both sides of the equation by -4 to solve for x:

x = -12 / -4

x = 3

Therefore, the solution to the equation is x = 3.

b) 2y - 3 = 10

To solve for y, we'll isolate the variable by moving the constant term to the other side:

2y = 10 + 3

Simplifying:

2y = 13

Dividing both sides of the equation by 2:

y = 13 / 2

y = 6.5

So the solution to the equation is y = 6.5.

c) 2(x + 1) = 3(x + 1)

First, we can distribute the coefficients to simplify the equation:

2x + 2 = 3x + 3

Next, we'll move the terms containing x to one side and the constant terms to the other side:

2x - 3x = 3 - 2

Simplifying:

-x = 1

Multiplying both sides of the equation by -1 to solve for x:

x = -1

Therefore, the solution to the equation is x = -1.

d) 5y + 10 = 5(2 + y)

First, we'll simplify the right side of the equation:

5y + 10 = 10 + 5y

Next, we'll move the constant terms to one side:

5y - 5y = 10 - 10

Simplifying:

0 = 0

The equation is an identity, which means it is true for all values of y. There is no specific solution for y in this case.

In summary: a) x = 3 b) y = 6.5 c) x = -1 d) No specific solution for y (identity equation).