Step 1: Solve the three inequalities in the options
A:
[tex]\begin{gathered} x+3\ge1 \\ \text{ Subtracting 3 from both sides we have} \\ x+3-3\ge1-3 \\ \text{this implies that} \\ x\ge-2 \end{gathered}[/tex]B:
[tex]\begin{gathered} 3x\ge1 \\ \text{ Dividing both sides by 3} \\ \frac{3x}{3}\ge\frac{1}{3} \\ x\ge\frac{1}{3} \end{gathered}[/tex]C:
[tex]\begin{gathered} x-3\ge1 \\ \text{Adding 3 to both sides we have} \\ x-3+3\ge1+3 \\ x\ge4 \end{gathered}[/tex]Step 2:
[tex]\text{ Pick an option whose solution is }x\ge4[/tex][tex]\text{Option C is the only inequality whose solution is }x\ge4[/tex]Hence, the right choice is C
