# Solve the congruence equation: 2x=3 mod 5

Solve the congruence equation:
2x=3 mod 5
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Step 1
the given congruence equation is $2x\equiv 3\left(\text{mod}5\right)$
the general congruence equation is $ax\equiv b\left(\text{mod}c\right)$
d=gcd(a,c)=gcd(2,5)=1
therefore, the equation has 1 solution
$2\left(1\right)\equiv 2!\equiv 3\left(\text{mod}5\right)$
$2\left(2\right)\equiv 4!\equiv 3\left(\text{mod}5\right)$
$2\left(3\right)\equiv 1!\equiv 3\left(\text{mod}5\right)$
$2\left(4\right)\equiv 3\left(\text{mod}5\right)$
therefore, the solution is x=4
Step 2
the solution of the given congruence equation is x=4