Answer:
x + [tex]\frac{1}{x}[/tex] = 15
Step-by-step explanation:
Given
3x + [tex]\frac{2}{x}[/tex] - 4 = 2(x + 9) - (7 - [tex]\frac{1}{x}[/tex] ) ← distribute and simplify right side
3x + [tex]\frac{2}{x}[/tex] - 4 = 2x + 18 - 7 + [tex]\frac{1}{x}[/tex]
3x + [tex]\frac{2}{x}[/tex] - 4 = 2x + 11 + [tex]\frac{1}{x}[/tex] ( subtract 2x from both sides )
x + [tex]\frac{2}{x}[/tex] - 4 = 11 + [tex]\frac{1}{x}[/tex] ( subtract [tex]\frac{1}{x}[/tex] from both sides )
x + [tex]\frac{1}{x}[/tex] - 4 = 11 ( add 4 to both sides )
x + [tex]\frac{1}{x}[/tex] = 15
