) 2xleqslant 1+x 3xgeqslant 6-3x

To solve the system of inequalities, we need to solve each inequality separately and then find the intersection of the solutions.<br /><br />Let's start with the first inequality: $2x \leqslant 1 + x$<br /><br />Subtract $x$ from both sides:<br />$2x - x \leqslant 1 + x - x$<br />$x \leqslant 1$<br /><br />Now let's move on to the second inequality: $3x \geqslant 6 - 3x$<br /><br />Add $3x$ to both sides:<br />$3x + 3x \geqslant 6 - 3x + 3x$<br />$6x \geqslant 6$<br /><br />Divide both sides by 6:<br />$\frac{6x}{6} \geqslant \frac{6}{6}$<br />$x \geqslant 1$<br /><br />Now we have the solutions for both inequalities:<br />$x \leqslant 1$ and $x \geqslant 1$<br /><br />The intersection of these solutions is $x = 1$.<br /><br />Therefore, the solution to the system of inequalities is $x = 1$.