To find an integer "x" that satisfies each equation, we need to find a value for "x" that makes the given expression congruent to zero modulo the specified modulus. In other words, we need to find a solution such that the expression is divisible by the modulus.

a.

Given data: 4x ≡ 2 (mod 3)

To find a solution for "x" in this equation, we need to find a value that, when multiplied by 4, gives a remainder of 2 when divided by 3.

Let's try different values of "x" until we find a solution:

x = 1: 4 * 1 ≡ 1 (mod 3) - Not congruent to 2 x = 2: 4 * 2 ≡ 2 (mod 3) - Congruent to 2

Hence, x = 2 is a solution to the equation 4x ≡ 2 (mod 3).

b.

Given data: 7x ≡ 4 (mod 9)

Similarly, we need to find a value for "x" that, when multiplied by 7, gives a remainder of 4 when divided by 9.

Let's try different values of "x":

x = 1: 7 * 1 ≡ 7 (mod 9) - Not congruent to 4 x = 2: 7 * 2 ≡ 5 (mod 9) - Not congruent to 4 x = 3: 7 * 3 ≡ 3 (mod 9) - Not congruent to 4 x = 4: 7 * 4 ≡ 1 (mod 9) - Not congruent to 4 x = 5: 7 * 5 ≡ 8 (mod 9) - Not congruent to 4 x = 6: 7 * 6 ≡ 6 (mod 9) - Not congruent to 4 x = 7: 7 * 7 ≡ 4 (mod 9) - Congruent to 4

Hence, x = 7 is a solution to the equation 7x ≡ 4 (mod 9).

c.

Given data: 5x ≡ 3 (mod 11)

Again, we need to find a value for "x" that, when multiplied by 5, gives a remainder of 3 when divided by 11.

Let's try different values of "x":

x = 1: 5 * 1 ≡ 5 (mod 11) - Not congruent to 3 x = 2: 5 * 2 ≡ 10 (mod 11) - Not congruent to 3 x = 3: 5 * 3 ≡ 4 (mod 11) - Congruent to 3

Hence, x = 3 is a solution to the equation 5x ≡ 3 (mod 11).