19. What is the solution set for -4x+10geqslant 5x+55

To solve the inequality $-4x + 10 \geqslant 5x + 55$, we need to isolate the variable $x$ on one side of the inequality.<br /><br />Step 1: Subtract $5x$ from both sides of the inequality:<br />$-4x + 10 - 5x \geqslant 5x + 55 - 5x$<br />$-9x + 10 \geqslant 55$<br /><br />Step 2: Subtract 10 from both sides of the inequality:<br />$-9x + 10 - 10 \geqslant 55 - 10$<br />$-9x \geqslant 45$<br /><br />Step 3: Divide both sides of the inequality by -9. Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign must be reversed:<br />$\frac{-9x}{-9} \leqslant \frac{45}{-9}$<br />$x \leqslant -5$<br /><br />Therefore, the solution set for the inequality $-4x + 10 \geqslant 5x + 55$ is $x \leqslant -5$.