The correct option is (A). The solution of the equation is x=48.125.
Given an equation [tex]x+\frac{x}{7}+\frac{1}{11}\left(x+\frac{x}{7}\right)=60[/tex].
A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.
Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get
[tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex]
Now, we will simplify the right-hand side equation by taking LCM, we get
[tex]\begin{aligned}\frac{77x+11x+7x+x}{77}&=60\\ \frac{96x}{77}&=60\end[/tex]
Further, we will multiply both sides with 77, we get
77×(96x/77)=77×60
96x=4620
Then, we will divide both sides with 96, we get
96x/96=4620/96
x=48.125
Hence, the solution of the given equation [tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex] is x=48.125.
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