Step-by-step explanation:
✧ [tex] \large{ \tt{ \: \frac{1}{2} x + 2 = \frac{3}{2} x - 6}}[/tex]
We need to get rid of the fractions. Notice that there are 4 terms in the equation. Multiply both sides of the equation by 2 to get rid of the fractions. Multiply by 2 because 2 is the denominator.
⤑ [tex] \large{ \tt{2( \frac{1}{2} x + 2) = 2( \frac{3}{2} x - 6)}}[/tex]
⤑ [tex] \large{ \tt{x + 4 = 3x - 12}}[/tex]
Subtract 4 from both sides in order to isolate the variable on the left.
⤑ [tex] \large{ \tt{x + 4 - 4 = 3x - 12 - 4}}[/tex]
⤑[tex] \large{ \tt{x = 3x - 16}}[/tex]
Move 3x to left hand side and change it's sign
⤑[tex] \large {\tt{x - 3x = - 16}}[/tex]
Subtract 3x from 1x
⤑ [tex] \large{ \tt{ - 2x = - 16}}[/tex]
Divide both sides of the equation by -2
⤑ [tex] \large{ \tt{ \frac{ - 2x}{ - 2} = \frac{ - 16}{ - 2}}} [/tex]
⤑ [tex] \large{ \tt{x = 8}}[/tex]
[tex] \boxed{ \boxed{ \underline{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \tt{x = 8}}}}}}}[/tex]
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