Question

Raj wrote the four equations that are shown below.

A
3(x+4)=3(x+2)+6

B
6(x-1)=3(x-1)+3

C
5x+4-x=2(2x-2)

D
-2(x+3)+x=-x-6

He examined them, without solving them, to determine which has no solution. Which of Raj’s equations has no solution?

Answer 1

the answer is C: 5x+4-x=2(2x-2)

Explanation:

Answer 2

C.

Explanation:

When a equation has no solution is because, inevitably, the variable gets eliminated. So, to find the answer to this question, we have to solve each of them

Option A.

`3(x+4)=3(x+2)+6`

`3x+12=3x+6+6\\3x-3x=12-12\\0=0`

As you can see, this equation is the one that doesn't have one solution, it actually have infinite solutions, because we got a true statement 0=0.

Option B.

`6(x-1)=3(x-1)+3\\6x-6=3x-3+3\\6x-3x=6\\3x=6\\x=2`

Option C.

`5x+4-x=2(2x-2)\\4x+4=4x-4\\4x-4x=-4-4\\0=-8`

We know that this result is false, this means the equation has no solutions, because it ended in a false statement.

Option D.

`-2(x+3)+x=-x-6\\-2x-6+x=-x-6\\-x+x=-6+6\\0=0`

It's the same as option A, this equation has infinite solutions.

Therefore, the equation that has no solution is C, because it ends in a false statement.