Study Guides | inequalities | Review 1: Ready To To On?

Study Guide: Review 1: Ready To To On?

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Describe the solution of each inequality in words.

1) $-2 \lt r$

All real numbers greater than -2

2) $t - 1 \le 7$

All real numbers less than or equal to 8

3) $2s \ge 6$

Method: Divide both sides by 2.
Simplified: $ s \ge 3 $
Conclusion: $s$ is all real numbers greater than or equal to $3$

4) $4 \gt 5 - x$

All real numbers greater than 1

Graph each inequality.

5) $x \gt -2$ <                                                                                     >

Open point on -2; arrow to the right

6) $m \ge 1\frac{1}{2}$ <                                                                                     >

Closed point on $1\frac{1}{2}$; arrow to the right

7) $g \gt \sqrt{8 + 1}$ <                                                                                     >

Open point on 3; arrow to the right

8) $h \ge 2^3$ <                                                                                     >

Closed point on 8; arrow to the right

Write the inequality shown by each graph.

9) <                      ●                                                               >
             -5    -4    -3    -2    -1    0    1    2    3    4    5    

$x \ge -3$

10) <                                                                             >
             -4    -3    -2    -1    0    1    2    3    4    5    6    

$x \lt 5$

11) <                                       ●                                               >
               -6    -5    -4    -3    -2    -1    0    1    2    3    4    

$x \le 1.5$

Write an inequality for each situation.

12) You must purchase at least 5 tickets to receive a discount.

$t \ge 5 $, where t is a natural number.

13) We have less than 13 years time to reduce global carbon pollution to pre-industrial levels.

$ a \lt 13 $, where a is positive.

14) A cell phone plan allows up to 250 minutes per month.

$m \le 250$, where m is not negative.

Solve each inequality and graph the solutions. Check your answers.

15) $ k + 5 \le 7 $

<                                                                                    >
$k \le 2$

16) $ 4 \gt p - 3 $

<                                                                                    >
$p \lt 7$

17) $ r - 8 \ge -12 $

<                                                                                    >
$r \ge -4$

18) $ -3 + p \lt-6 $

<                                                                                    >
$p \lt -3$

19) Allie must sell at least 50 gift baskets for the band fundraiser. She already sold 36 baskets. Write and solve an inequality to determine how many more baskets Allie must sell for the fundraiser.

$ 36 + b \ge 150 $ → $ b \ge 14 $; Allie must sell at least 14 more baskets.

20) Dante has budgeted at most \$120 per month to donate to the local food banks and shelters. So far this month, he has already given \$40. Write and solve an inequality to determine how much more Dante can give for the rest of the month.

Solve each inequality and graph the solutions. Check your answers.

$40 + m \le 120$; Dante can donate up to $80 more this month.

21) $ -4x \lt 8 $

<                                                                                    >
$x \gt -2$

22) $ \frac{d}{3} \ge -3 $

<                                                                                    >
$d \ge -9$

23) $ \frac{3}{4}t \le 12 $

<                                                                                    >
$t \le 16$

24) $ 8 \gt -16c $

<                                                                                    >
$c \gt -\frac{1}{2}$

25) A spool of ribbon is 80 inches long. James needs to cut strips of ribbon that are 14 inches long. What are te possible numbers of strips that James can cut?

Equation: $14r \le 80$
Simplified: $r \le 5.7$
Conclusion
James can cut 0, 1, 2, 3, 4, or 5 strips of ribbon.
  1. All real numbers greater than -2

  2. All real numbers less than or equal to 8

  3. All real numbers greater than or equal to 3

  4. All real numbers greater than 1

  5. Open point on -2; arrow to the right

  6. Closed point on $1\frac{1}{2}$; arrow to the right

  7. Open point on 3; arrow to the right

  8. Closed point on 8; arrow to the right

  9. $x \ge -3$

  10. $x \lt 5$

  11. $x \le 1.5$

  12. $t \ge 5 $, where t is a natural number.

  13. $ a \lt 13 $, where a is positive.

  14. $m \le 250$, where m is not negative.

  15. $k \le 2$

  16. $p \lt 7$

  17. $r \ge -4$

  18. $p \lt -3$

  19. $36 + b \ge 150$ → $b \ge 14$; Allie must sell at least 14 more baskets.

  20. $40 + m \le 120$; Dante can donate up to $80 more this month.

  21. $x \gt -2$

  22. $d \ge -9$

  23. $t \le 16$

  24. $c \gt -\frac{1}{2}$

  25. $14r \le 80$; $r \le 5.7$; James can cut 0, 1, 2, 3, 4, or 5 strips of ribbon.

Source: https://class.ronliskey.com/study/mathematics-8/8-3-q1-ready-to-go-on/