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:

$6x+9=12\Rightarrow6x=12-9\Rightarrow6x=3\Rightarrow\frac{6x}{6}=\frac{3}{6}\Rightarrow x=\frac{3}{6}=\frac{1}{2}$

And

$2x+3=4\Rightarrow2x=4-3\Rightarrow2x=1\Rightarrow\frac{2x}{2}=\frac{1}{2}\Rightarrow x=\frac{1}{2}$

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