Solve the following inequality: -3x+(3)/(2)geqslant -(x-6)-x Answer Athemptiont of square disappointed

To solve the inequality $-3x+\frac {3}{2}\geqslant -(x-6)-x$, we first simplify the right side of the inequality:<br /><br />$-3x+\frac {3}{2}\geqslant -(x-6)-x$<br /><br />$-3x+\frac {3}{2}\geqslant -x+6-x$<br /><br />$-3x+\frac {3}{2}\geqslant -2x+6$<br /><br />Next, we isolate the variable $x$ by adding $2x$ to both sides of the inequality:<br /><br />$-3x+2x+\frac {3}{2}\geqslant -2x+2x+6$<br /><br />$-x+\frac {3}{2}\geqslant 6$<br /><br />Then, we subtract $\frac {3}{2}$ from both sides of the inequality:<br /><br />$-x+\frac {3}{2}-\frac {3}{2}\geqslant 6-\frac {3}{2}$<br /><br />$-x\geqslant \frac {9}{2}$<br /><br />Finally, we multiply both sides of the inequality by $-1$ to solve for $x$:<br /><br />$-1(-x)\leqslant -1(\frac {9}{2})$<br /><br />$x\leqslant -\frac {9}{2}$<br /><br />Therefore, the solution to the inequality is $x\leqslant -\frac {9}{2}$.