Question

1) 7a - 10 = 2 - 4a; 2) 3p - 1 - (p + 3) = 1; 3) 6(1 + 5x) = 5(1 + 6x).

Answer 1

1) 7а-10=2-4а

7а+4а=2+10

11а=12

а=12/11

2)3р-1-(р+3)=1

3р-1-р-3=1

3р-р=1+1+3

2р=5

р=2,5

3)6(1 + 5x) = 5(1 + 6x)

6+30х=5+30х

30х-30х=5-6

0х=-1

нет корней, так как 0х

Answer 2

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

1. 7a - 10 = 2 - 4a

To solve this equation, we'll start by simplifying both sides and then isolating the variable "a."

Adding 4a to both sides:

7a + 4a - 10 = 2 - 4a + 4a

Combining like terms:

11a - 10 = 2

Now, let's isolate the variable "a" by adding 10 to both sides:

11a - 10 + 10 = 2 + 10

Simplifying:

11a = 12

Finally, we divide both sides by 11 to solve for "a":

a = 12/11

So the solution to the equation is a = 12/11.

2. 3p - 1 - (p + 3) = 1

To solve this equation, we'll start by simplifying the expression within the parentheses first:

3p - 1 - p - 3 = 1

Combine like terms:

(3p - p) - (1 + 3) = 1

2p - 4 = 1

Next, we'll isolate the variable "p" by adding 4 to both sides:

2p - 4 + 4 = 1 + 4

Simplifying:

2p = 5

Finally, divide both sides by 2 to solve for "p":

p = 5/2

Therefore, the solution to the equation is p = 5/2.

3. 6(1 + 5x) = 5(1 + 6x)

Let's start by distributing the multiplication on both sides:

6 + 30x = 5 + 30x

Now, we can see that the expression "30x" appears on both sides. By subtracting 30x from both sides, it will cancel out:

6 + 30x - 30x = 5 + 30x - 30x

Simplifying:

6 = 5

However, we've reached an inconsistency. The equation 6 = 5 is not true, which means that there is no solution to this equation.

In summary:

1. The solution to the equation 7a - 10 = 2 - 4a is a = 12/11.
2. The solution to the equation 3p - 1 - (p + 3) = 1 is p = 5/2.
3. The equation 6(1 + 5x) = 5(1 + 6x) has no solution.