Answer:
The answer is x = 8.
Step-by-step explanation:
LCD is the least common denominator of fractions. LCD represents the smallest number that can be used as a common denominator for a particular set of fractions.
The given equation is [tex]\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x}[/tex]
Here we can take LCD as 4x because 4x is divisible by 2x as [tex]\frac{4x}{2x} = 2[/tex], 4x is divisible by 4 as [tex]\frac{4x}{4} = 1[/tex]
therefore we can write
[tex]\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{10}{4x} + \frac{x}{4x} = \frac{18}{4x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{x + 10}{4x} = \frac{18}{4x}[/tex]
now we can eliminate the LCD from both sides of the equation and we get
x + 10 = 18 [tex]\therefore[/tex] x = 18 - 10 [tex]\therefore[/tex] x = 8.
