What is the solution set of x+2geqslant 6 and 3xgeqslant 6 x is greater than or equal to 4 x is less than 4 x is equal to 2 x is less than or equal to 2 B This is a required question

To solve the system of inequalities $x+2\geqslant 6$ and $3x\geqslant 6$, we need to solve each inequality separately and then find the intersection of the solution sets.<br /><br />For the first inequality $x+2\geqslant 6$, we can subtract 2 from both sides to isolate $x$:<br />$x+2-2\geqslant 6-2$<br />$x\geqslant 4$<br /><br />For the second inequality $3x\geqslant 6$, we can divide both sides by 3 to isolate $x$:<br />$\frac{3x}{3}\geqslant \frac{6}{3}$<br />$x\geqslant 2$<br /><br />Now, we need to find the intersection of the solution sets for both inequalities. The solution set for the first inequality is $x\geqslant 4$, and the solution set for the second inequality is $x\geqslant 2$. The intersection of these two solution sets is $x\geqslant 4$.<br /><br />Therefore, the solution set for the system of inequalities $x+2\geqslant 6$ and $3x\geqslant 6$ is $x\geqslant 4$.