Question

2. Which equation is equivalent to the equation 6x + 9 = 12?X + 9 = 62x + 3 = 43x + 9 = 66x + 12 = 9

Answer 1

To answer this question, we can see that if we multiply the next equation line by 3, we have that:

`3\cdot(2x+3=4)=3\cdot2x+3\cdot3=3\cdot4\Rightarrow6x+9=12`

Therefore, we can say that both equations are equivalent.

We can check this if we solve the value of x for both equations. The result must be the same:

`6x+9=12\Rightarrow6x=12-9\Rightarrow6x=3\Rightarrow(6x)/(6)=(3)/(6)\Rightarrow x=(3)/(6)=(1)/(2)`

And

`2x+3=4\Rightarrow2x=4-3\Rightarrow2x=1\Rightarrow(2x)/(2)=(1)/(2)\Rightarrow x=(1)/(2)`

Therefore, the equation that is equivalent to the equation 6x + 9 = 12 is 2x+3 = 4 (second option).