Answer: C
Step-by-step explanation:
In order to have no solution, we will not have "x=" as an answer. All we have to do is to solve for x in each option.
Option A: Incorrect
[tex]2x-6x=4(1-x)-4[/tex] [combine like terms]
[tex]-4x=4-4x-4[/tex] [combine like terms]
[tex]-4x=-4x[/tex]
Even if we didn't solve for x, notice that both sides of the equation is the same. That means that there will be infinite solutions. Therefore, this option is incorrect.
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Option B: Incorrect
[tex]6x-2x=4(1-x)-4[/tex] [combine like terms]
[tex]4x=4(1-x)-4[/tex] [distribute]
[tex]4x=4-4x-4[/tex] [combine like terms]
[tex]4x=-4x[/tex] [add both sides by 4x]
[tex]8x=0[/tex] [divide both sides by 8]
[tex]x=0[/tex]
Notice that we got an actual value for x. Therefore, this option is incorrect.
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Option C: Correct
[tex]2x-6x=4(1-x)[/tex] [combine like terms]
[tex]-4x=4(1-x)[/tex] [distribute]
[tex]-4x=4-4x[/tex] [add both sides by 4x]
[tex]0=4[/tex]
Notice that x is gone all together. With what we have left, 0=4 is not true. Therefore, this option is correct with having no solutions.
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Option D: Incorrect
[tex]6x-2x=4(1-x)[/tex] [combine like terms]
[tex]4x=4(1-x)[/tex] [distribute]
[tex]4x=4-4x[/tex] [add both sides by 4x]
[tex]8x=4[/tex] [divide both sides by 8]
[tex]x=\frac{4}{8}[/tex] [simplify]
[tex]x=\frac{1}{2}[/tex]
Notice that we got an actual value for x. Therefore, this option is incorrect.
