Question

Из данных равенств выберите тождество: 1) 4y-8 =4(y-2); 2) х+(х-4)=3х-4; 3) a-b+c=-(b-a-c); 4) 9a-(b+c)=9a-b-c; 5) 2y-6=2(y-1); 6) 2,5x+1,7x-3,2x=x. Помогите пойдалуста!

Answer 1

1)4y-8=4(y-2)
4(y-2)=4(y-2)
4)9a-(b+c)=9a-b-c
9a-b-c=9a-b-c

Answer 2

Task: Select the identity from the given equations:

To determine the identity from the given equations, let's analyze each equation one by one:

1) 4y - 8 = 4(y - 2) - To solve this equation, we can distribute the 4 on the right side of the equation: 4y - 8 = 4y - 8. - As we can see, the equation is true for all values of y. Therefore, the given equation is an identity.

2) x(x - 4) = 3x - 4 - To solve this equation, we can expand the left side of the equation: x^2 - 4x = 3x - 4. - By rearranging the terms, we get: x^2 - 7x + 4 = 0. - This is a quadratic equation, and it does not hold true for all values of x. Therefore, the given equation is not an identity.

3) a - b + c = -(b - a - c) - To solve this equation, we can simplify both sides of the equation: a - b + c = -b + a + c. - As we can see, the equation is true for all values of a, b, and c. Therefore, the given equation is an identity.

4) 9a - (b + c) = 9a - b - c - To solve this equation, we can simplify both sides of the equation: 9a - b - c = 9a - b - c. - As we can see, the equation is true for all values of a, b, and c. Therefore, the given equation is an identity.

5) 2y - 6 = 2(y - 1) - To solve this equation, we can distribute the 2 on the right side of the equation: 2y - 6 = 2y - 2. - By rearranging the terms, we get: -6 = -2. - This equation is not true, as -6 is not equal to -2. Therefore, the given equation is not an identity.

6) 2.5x + 1.7x - 3.2x = x - To solve this equation, we can combine like terms on the left side of the equation: 0 = x. - As we can see, the equation is true for all values of x. Therefore, the given equation is an identity.

In summary, the identities from the given equations are: 1) 4y - 8 = 4(y - 2) 3) a - b + c = -(b - a - c) 4) 9a - (b + c) = 9a - b - c 6) 2.5x + 1.7x - 3.2x = x

Please let me know if you need any further assistance!