Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 482. \( 15 k \leq-40 \) 483. \( 35 k \geq-77 \) 484. \( 23 p-2(6-5 p)>3(11 p-4) \) 485. \( 18 q-4(10-3 q)<5(6 q-8) \) 486. \( -\frac{9}{4} x \geq-\frac{5}{12} \) 487. \( -\frac{21}{8} y \leq-\frac{15}{28} \) 488. \( c+34<-99 \) 489. \( d+29>-61 \)

Here are the solutions to the inequalities: 1. **482. \( 15k \leq -40 \)** - **Solution:** \( k \leq -\frac{8}{3} \) - **Graph:** Closed dot at \( -\frac{8}{3} \), shaded left. - **Interval Notation:** \( (-\infty,\, -\frac{8}{3}] \) 2. **483. \( 35k \geq -77 \)** - **Solution:** \( k \geq -\frac{11}{5} \) - **Graph:** Closed dot at \( -\frac{11}{5} \), shaded right. - **Interval Notation:** \( \left[-\frac{11}{5},\, \infty\right) \) 3. **484. \( 23p - 2(6 - 5p) > 3(11p - 4) \)** - **Solution:** No solution. - **Graph:** No shading. - **Interval Notation:** \( \varnothing \) 4. **485. \( 18q - 4(10 - 3q) < 5(6q - 8) \)** - **Solution:** No solution. - **Graph:** No shading. - **Interval Notation:** \( \varnothing \) 5. **486. \( -\frac{9}{4}x \geq -\frac{5}{12} \)** - **Solution:** \( x \leq \frac{5}{27} \) - **Graph:** Closed dot at \( \frac{5}{27} \), shaded left. - **Interval Notation:** \( \left(-\infty,\, \frac{5}{27}\right] \) 6. **487. \( -\frac{21}{8}y \leq -\frac{15}{28} \)** - **Solution:** \( y \geq \frac{10}{49} \) - **Graph:** Closed dot at \( \frac{10}{49} \), shaded right. - **Interval Notation:** \( \left[\frac{10}{49},\, \infty\right) \) 7. **488. \( c + 34 < -99 \)** - **Solution:** \( c < -133 \) - **Graph:** Open dot at \( -133 \), shaded left. - **Interval Notation:** \( (-\infty,\, -133) \) 8. **489. \( d + 29 > -61 \)** - **Solution:** \( d > -90 \) - **Graph:** Open dot at \( -90 \), shaded right. - **Interval Notation:** \( \left(-90,\, \infty\right) \) If you have any questions or need further assistance, feel free to ask!