1/2 (c-3) + 3/4c>1/2 (2c+3) + 3/8

Simplify 1/2 (c - 3) to c - 3/2

c - 3/2 + 3/4c > 1/2 (2c + 3) + 3/8

Simplify 3/4c to 3c/4

c - 3/2 + 3c/4 > 1/2 (2c + 3) + 3/8

Simplify 1/2 (2c + 3) to 2x + 3/2

c - 3/2 + 3c/4 > 2c + c/2 + 3/8

Multiply both sides by 4 (The LCM of 2, 4)

2 (c - 3) + 3c > 2 (2c + 3) + 3/2

Expand

2x - 6 + 3c > 4c + 6 + 3/2

Simplify 2c - 6 + 3c to 5c - 6

5c - 6 > 4c + 6 + 3/2

Simplify 4c + 6 + 3/2 to 4c + 15/2

5c - 6 > 4c + 15/2

Add 6 to both sides

5c > 4c + 15/2 + 6

Simplify 4c + 15/2 + 6 to 4c + 27/2

5c > 4c + 27/2

Subtract 4c from both sides

5c - 4c > 27/2

Simplify 5c - 4c to c

c > 27/2