Question

5(х+7)-6(х-5)=12 ; 5(2х+1)-2(4х+3)=2х-1

Answer 1

5(x+7)-6(x-5)=12
5x+35-6x-5=12
5x-6x=-35+5+12
-x=-18
x=18

5(2x+1)-2(4x+3)=2x-1
10x+5-8x-6=2x-1
10x-8x-2x=-5+6-1
x=0

Answer 2

Let's solve each equation step by step:

1. 5(x + 7) - 6(x - 5) = 12

Expand the parentheses:

5x + 35 - 6x + 30 = 12

Combine like terms:

(5x - 6x) + (35 + 30) = 12

-x + 65 = 12

Move the constant term to the right side:

-x = 12 - 65

-x = -53

Multiply both sides by -1 to isolate x:

x = -1(-53)

x = 53

Therefore, the solution to the first equation is x = 53.

2. 5(2x + 1) - 2(4x + 3) = 2x - 1

Expand the parentheses:

10x + 5 - 8x - 6 = 2x - 1

Combine like terms:

(10x - 8x) + (5 - 6) = 2x - 1

2x - 1 = 2x - 1

The equation simplifies to 2x - 1 = 2x - 1, which means that the equation is true for all values of x. In this case, the equation does not provide a unique solution.

Therefore, the second equation has infinitely many solutions.