John wrote that 5 + 5 = 10. then wrote that 5 + 5 + n = 10 + n. are the equations john wrote equivalent? explain.

Equation 5 + 5 = 10  and 5 + 5 + n = 10 + n are equivalent equation

Given that  

John wrote that 5 + 5 = 10   (1)

Then wrote that 5 + 5 + n = 10 + n     (2)

Need to determine are the equations written by John are equivalent.

First we need to keep in mind that whenever we apply same operation like addition, subtraction, multiplication and division on both the sides of equation that is left hand side and right hand side, we get the equivalent equation.

As in the second equation John added same value that is n on both sides of equation, we can say that equation with n is equivalent to the previous equation without n

Other way is let’s solve equation (2) and see if we can get equation (1)

5 + 5 + n = 10 + n  

On subtracting both the sides with n we get,

5 + 5 + n – n = 10 + n – n

=> 5 + 5 = 10 which is same as equation (1)

Hence we can conclude that equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation.

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step-by-step explanation:

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