1. **State the problem:** We need to determine which values of $c$ satisfy the inequality $$6c + 4 < 75.$$\n\n2. **Write the inequality and solve for $c$: **\n$$6c + 4 < 75$$\nSubtract 4 from both sides:\n$$6c + \cancel{4} - \cancel{4} < 75 - 4$$\n$$6c < 71$$\nDivide both sides by 6:\n$$\frac{6c}{\cancel{6}} < \frac{71}{6}$$\n$$c < \frac{71}{6} \approx 11.83$$\n\n3. **Interpretation:** Any value of $c$ less than approximately 11.83 satisfies the inequality.\n\n4. **Check each given value:**\n- $c=7$: $6(7)+4=42+4=46 < 75$ ✓\n- $c=1$: $6(1)+4=6+4=10 < 75$ ✓\n- $c=3$: $6(3)+4=18+4=22 < 75$ ✓\n- $c=4$: $6(4)+4=24+4=28 < 75$ ✓\n\n**All given values satisfy the inequality.**