Question

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

Answer 1

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

$2 \neq -4$

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

$-1 \neq 5$

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

$15 \neq 10$

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