Does each equation have at least one solution? (no or yes questions)

1. -8x+2= -8x-4
2. 12-x=5x+12
3. 6x+9=6x+9
4. 15-x=10-x

None of the given equation has at least one solution

1) -8x + 2 = -8x - 4 ⇒ no

2) 12 - x = 5x + 12 ⇒ no

3) 6x + 9 = 6x + 9 ⇒ no

4) 15 - x = 10 - x  ⇒ no

Solution:

1) -8x + 2 = -8x - 4

In the above equation, -8x gets cancel each other on both sides

-8x + 2 = -8x - 4

There is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”

2) 12 - x = 5x + 12

In the above equation, 12 gets cancel each other on both sides

-x = 5x

There is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”

3) 6x + 9 = 6x + 9

In the above equation, 6x + 9 gets cancel each other on both sides

There is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”

4) 15 - x = 10 - x

In the above equation, -x gets cancel each other on both sides

There is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this