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# Linear Congruences

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Find the solutions of
(a) 4x is congruent to 3(mod 7)
(b) 9x is congruent to 11(mod 26)
(c) 3x + 1 is congruent to 4(mod 5)
(d) 8x is congruent to 6(mod 14).

https://brainmass.com/math/basic-algebra/linear-congruences-16597

#### Solution Preview

LINEAR CONGRUENCES ( Part I)

Written by :-Thokchom Sarojkumar Sinha

Find the solutions of
(a) 4x ≡ 3(mod 7)
(b) 9x ≡ 11(mod 26)
(c) 3x + 1 ≡ 4(mod 5)
(d) 8x ≡ 6(mod 14)

Solution :- 4x ≡ 3(mod 7)

(4,7) = 1

From We find
7 = 4.1 + 3 1 = 4 - 3.1
4 = 3.1 + 1 = 4 - (7 - ...

#### Solution Summary

This solution is comprised of a detailed explanation for finding the solutions of linear congruences.

It contains step-by-step explanation for finding the solutions of
a) 4x is congruent to 3(mod 7)
(b) 9x is congruent to 11(mod 26)
(c) 3x + 1 is congruent to 4(mod 5)
(d) 8x is congruent to 6(mod 14).

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