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

$x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60$

Now, we will simplify the right-hand side equation by taking LCM, we get

$\begin{aligned}\frac{77x+11x+7x+x}{77}&=60\\ \frac{96x}{77}&=60\end$

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 $x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60$ is x=48.125.

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