Pls. Answer correctly and complete solution.

Topic : Solving Congruence Equations.

Solving Congruence Equations * Solving a congruence equation means finding all the whole number values of the variable for which the congruence is true. Example: Solve for x: 1. 3x + 4= 5 mod 8 Solution: X = 0 3(0) + 4 # 5 mod 8 x =1 3(1) + 4 # 5 mod 8 x = 2 3(2) + 4 # 5 mod 8 x = 3 3(3) + 4 = 5 mod 8 X =4 3(4) + 4 # 5 mod 8 x = 5 3(5) + 4 # 5 mod 8 X = 6 3(6) + 4 # 5 mod 8 X =7 3(7) + 4 # 5 mod 8 . x =3 Ans. Initial solution (3, 11, 19, 27, 35, 43, 51...) Infinite solution 2. Solve for x: 4x + 7= 3 mod 10 Solution: Let x = 0 4(0) + 7 # 3 mod 10 ? X =1 4(1) + 7 # 3 mod 10? x = 2 4(2) + 7 # 3 mod 10 ? X=3 4(3) + 7 # 3 mod 10 ? X = 4 4(4) + 7 = 3 mod 10? X = 5 4(5) + 7 # 3 mod 10? X = 6 4(6) + 7 # 3 mod 10? X =7 4(7) + 7 # 3 mod 10? X =8 4(8) + 7 # 3 mod 10? V X = 9 4(9) + 7 = 3 mod 10 ? x =(4, 9) Initial Solution (4, 9, 14, 19, 24, 29, ... ) Infinite Solution 3. 3x + 2 = 4 mod 6 Solution: Let x = 0 3(0) + 2 # 4 mod 6 x =1 3(1) + 2 # 4 mod 6 X =2 3(2) + 2 # 4 mod 6 x = 3 3(3) + 2 # 4 mod 6 X =4 3(4) + 2 # 4 mod 6 X = 5 3(5) + 2 # 4 mod 6 No Solution Ans.IV. Find all whole numbers solution of the congruence equation. 1. x = 10 mod 3 6. (3x+1) = 4 mod 9 2. x = 12 mod 5 7. (2x+2) = 6 mod 4 3. 2x = 12 mod 5 8. (5x+4) = 2 mod 8 4. 3x = 8 mod 11 9. (3x+12) = 7 mod 10 5. 4x = 5 mod 13 10. (2x+3) = 8 mod 12