Question

Select all equations that are equivalent to(5x+6)2= 3 - (4x + 12)5x + 6 = 3 - (4.c +12)(53+6)2= -43 - 9x + 3 = 3 – (4x + 12)(5x+6)2= -43 + 155x + 6 = -82 - 18

Answer 1

1) Since we have this equation let's work on that to find equivalent equations

`\begin{gathered} ((5x+6))/(2)=3-(4x+12) \\ \text{Multiply both sides by 2} \\ (5x+6)\text{ = 6 -}2(4x+12) \\ (5x\text{ +6) = }6\text{ -8x -24} \\ 5x\text{ +6 =-8x-18} \end{gathered}`

2) Now let's compare that, we have the last one as equivalent.

`5x\text{ +6 =-8x-18}`

If we look at the third one, we can see that only on the left side:

`\begin{gathered} (5x+6)/(2)=\text{ }(5x)/(2)\text{ +}(6)/(2) \\ \text{Then} \\ (5x)/(2)\text{ +}(6)/(2)=3-(4x+12)\text{ } \end{gathered}`

And finally, the second one, just working on the right side:

`\begin{gathered} (5x+6)/(2)=3-(4x+12) \\ (5x+6)/(2)=3-4x-12 \\ (5x+6)/(2)=-4x-9 \end{gathered}`

3) So the equivalent ones are the second, the third, and the fifth one.