1. Problem: Solve each inequality below, then match to the graph that represents its solution set. 1. Solve $x + 11 > 16$: Subtract 11 from both sides: $$x + 11 - 11 > 16 - 11$$ $$x > 5$$ The solution is all $x$ greater than 5, so on the number line this is an arrow pointing right starting just above 5. 2. Solve $x - 6 < 1$: Add 6 to both sides: $$x - 6 + 6 < 1 + 6$$ $$x < 7$$ This means all $x$ less than 7. 3. Solve $x + 2 \leq -3$: Subtract 2 from both sides: $$x + 2 - 2 \leq -3 - 2$$ $$x \leq -5$$ This is all $x$ less than or equal to -5. 4. Solve $x + 3 \geq 1$: Subtract 3: $$x + 3 - 3 \geq 1 - 3$$ $$x \geq -2$$ 5. Solve $x - 1 < -7$: Add 1: $$x - 1 + 1 < -7 + 1$$ $$x < -6$$ Match graphs: - For $x > 5$ (1), the graph must show values greater than 5. Among given graphs c and e go right from 0 and 0 respectively, so c which goes 0 to 8 arrow right matches. - For $x < 7$ (2), all less than 7, but upper bound is near 8; matches graph e (arrow left near 8). - For $x \leq -5$ (3), less than or equal to -5, matches a (arrow left -8 to 0). - For $x \geq -2$ (4), greater or equal to -2, matches b (arrow right -4 to 4). - For $x < -6$ (5), less than -6, matches d (arrow right from -8 to 0 but near -8, maybe a typo, so matches a better). 6. Solve $d - 5 \leq 1$: Add 5: $$d \leq 6$$ Graph: arrow left at 6. 7. Solve $s + 9 < 8$: Subtract 9: $$s < -1$$ 8. Solve $a - 7 \geq -13$: Add 7: $$a \geq -6$$ 9. Solve $w - 1 < 4$: Add 1: $$w < 5$$ 10. Solve $4 \geq k + 3$: Subtract 3: $$1 \geq k$$ $$k \leq 1$$ 11. Solve $-9 \leq b - 4$: Add 4: $$-5 \leq b$$ $$b \geq -5$$ 12. Solve $-2 \geq x + 4$: Subtract 4: $$-6 \geq x$$ $$x \leq -6$$ 13. Solve $2y < y + 2$: Subtract $y$: $$2y - y < y + 2 - y$$ $$y < 2$$ 14. Define variable $n$. "A number decreased by 10 is greater than -5": $$n - 10 > -5$$ $$n > 5$$ 15. Variable $m$. "A number increased by 1 is less than 9": $$m + 1 < 9$$ $$m < 8$$ 16. Variable $x$. "Seven more than a number is less than or equal to -18": $$x + 7 \leq -18$$ $$x \leq -25$$ 17. Variable $y$. "Twenty less than a number is at least 15": $$y - 20 \geq 15$$ $$y \geq 35$$ 18. Variable $a$. "A number plus 2 is at most 1": $$a + 2 \leq 1$$ $$a \leq -1$$ --- Second Set: 1. Solve $-8 \geq x - 15$: Add 15: $$7 \geq x$$ $$x \leq 7$$ 2. Solve $4x + 3 < 5x$: Subtract $4x$: $$3 < x$$ $$x > 3$$ 3. Solve $8x > 7x - 4$: Subtract $7x$: $$x > -4$$ 4. Solve $12 + x \leq 9$: Subtract 12: $$x \leq -3$$ Match graphs: - $x \leq 7$ (1) matches b (0 to 8 arrow right). - $x > 3$ (2) matches b from 0 to 8 arrow right starting above 3. - $x > -4$ (3) matches a (-6 to 2 arrow right from just above -4). - $x \leq -3$ (4) matches d (0 to 8 arrow left from 0, but 0 to 8 left arrow isn't below -3, best match is c left from -8 to 0). 5. Solve $r - (-5) > -2$: $$r + 5 > -2$$ Subtract 5: $$r > -7$$ 6. Solve $3x + 8 \geq 4x$: Subtract $3x$: $$8 \geq x$$ $$x \leq 8$$ 7. Solve $n - 2.5 \geq -5$: Add 2.5: $$n \geq -2.5$$ 8. Solve $1.5 < y + 1$: Subtract 1: $$0.5 < y$$ $$y > 0.5$$ 9. Solve $z + 3 > \frac{2}{3}$: Subtract 3: $$z > -\frac{7}{3}$$ 10. Solve $\frac{1}{2} \leq c - \frac{3}{4}$: Add $\frac{3}{4}$: $$\frac{1}{2} + \frac{3}{4} \leq c$$ $$\frac{5}{4} \leq c$$ $$c \geq 1.25$$ 11. "The sum of a number and 17 is no less than 26": $$n + 17 \geq 26$$ $$n \geq 9$$ 12. "Twice a number minus 4 is less than three times the number": Let $x$ be the number: $$2x - 4 < 3x$$ Subtract $2x$: $$-4 < x$$ $$x > -4$$ 13. "Twelve is at most a number decreased by 7": $$12 \leq x - 7$$ Add 7: $$19 \leq x$$ $$x \geq 19$$ 14. "Eight plus four times a number is greater than five times the number": $$8 + 4x > 5x$$ Subtract $4x$: $$8 > x$$ $$x < 8$$ 15. Plane altitude problem: Plane altitude = $5.8$ miles Troposphere depth = $8.6$ miles Remaining height before leaving troposphere: $$8.6 - 5.8 = 2.8$$ 16. Soil cushion problem: Topsoil depth = 30 cm Bush hole depth = 18 cm Current cushion = 8 cm Remaining depth for cushion: $$30 - 18 = 12$$ cm total cushion allowed Remaining cushion addition: $$12 - 8 = 4$$ cm Final answers summarized: "q_count":16