Does the congruence equation

6x ≡ 7(mod 25)

have a solution for x (notice that congruence only makes sense if x ∈ z so you are looking for integer

solutions)? if it does, find the solution. if it does not, prove that it does not.

The solution to the congruence equation  6x ≡ 7(mod 25)  is x = 22.

We have the congruence equation

6x ≡ 7(mod 25)

6x ≡ 25n + 7  where x and n are integers.

So, it means 25 divides 6x-7.

As 25 divides 6x-7 . So value of x should be greater than 5.

It does not work for 6,7,..... 21.  

For x=22

The solution for the congruence equation 6x ≡ 7(mod 25) is x=22.

Learn more:link

x = 22.

Step-by-step explanation:

6x ≡ 7(mod 25)

6x ≡ 25n + 7  where x and n are integers.

Checking multiples of 25:

25:  (n= 1)   25+7 = 32. 6*5 = 2 (mod 25) . Does not fit.

50, 75 , 100  do not fit either.

The answer  is 22 because 6*22 = 132 =  125 + 7 = 7(mod 25).

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get