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Linear Congruence

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Please help me solve this congruence:

21x = 4 (mod 76).

I do not know how to reduce/change mods like when they go from 8x = 6 (mod 14) to x=6 mod 7. I do not understand this, so please describe every single step in your solution when you do stuff like that. I do know how to find the GCD of 2 numbers so you do not need to teach me that.

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The expert helps solve a congruence. A complete, neat and step-by-step solution is provided.

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21x = 4 (mod 76) means (21x - 4) is divisible by 76.

This means 21x - 4 = 76k, where k is an integer.

21x = 4 + 76k

x = (4 + 76k)/21

The first trial integer value for k such that even x will turn out to be an integer is k = 11.

When we plug in k = 11 and find x, we get x = 40.

The next is k = 32.

When we plug in k = 32 and find x, we ...

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