Answer:
Only option E is equivalent to [tex]5x+6=-8x-18[/tex].
Step-by-step explanation:
Given the expression
(5x+6) over 2 = 3-(4x + 12)
Let us simplify the expression
[tex]\frac{\left(5x+6\right)}{2}=3-\left(4x+12\right)[/tex]
Multiply both sides by 2
[tex]\frac{5x+6}{2}\cdot \:2=3\cdot \:2-\left(4x+12\right)\cdot \:2[/tex]
[tex]5x+6=6-\left(4x+12\right)\cdot \:2[/tex]
Expand -(4x + 12) = -4x - 12
[tex]5x+6=-8x-18[/tex]
Thus, option E is equivalent to [tex]5x+6=-8x-18[/tex].
Further solving
[tex]5x+6=-8x-18[/tex]
Add 8x from to both sides
[tex]5x+8x=-8x-24+8x[/tex]
Simplify
[tex]13x=-24[/tex]
Divide both sides
[tex]\frac{13x}{13}=\frac{-24}{13}[/tex]
Simplify
[tex]x=-\frac{24}{13}[/tex]
Thus, only option E is equivalent to [tex]5x+6=-8x-18[/tex].
