- a. If 56 + 58 = t, does t = 56 + 58?
b. If 56 + 58 < r, is r < 56 + 58? Justify your answer.
c. Explain th e differences betw een th ese two examples. - Th i n k A b o u t a Pl an You w ant to qualify for a regional diving
com petition. At today’s com petition, you m u st score at least 53 points.
Out of a possible 10 points, your scores on each of th e first 5 dives are
show n at th e right. W hat scores can you ea rn on the arm stan d dive th at
will qualify you for the regional diving com petition?- W hat inform ation do you know? W hat inform ation do you need?
- How m ight w riting an d solving an inequality help you?
- W hat does th e solution of the inequality m e a n in term s of the
original situation?
- Quali f ying Scores To en ter a com petition, stu d en ts m u st score a total of at least
450 points on five qualifying tests. Each test is w orth 100 points. On th e first four
tests, your scores were 94, 88 , 79, an d 95. W hat are th ree possible scores you can
ea rn on th e last test to en ter the com petition?
Er r o r A n a l y s i s Describe and correct the error in solving each inequality or in
graphing the solution.
70.OFFICIAL SCORE CARD
DIVE SCORE
Front Dive 9.8
Back Dive 8.9
Reverse Dive 8.4
In w a rd Dive 8.2
Twisting Dive 9.4
Armstand Dive^7- a. Open-Ended Use each of th e inequality sym bols < , < , > an d > to write
four inequalities involving addition or subtraction,
b. Solve each inequality from p a rt (a) an d graph your solutions.
^ 73. a. M allory says th at she can solve the inequality a + 3.2 > 8.6 by replacing a w i t h
5, 6 , an d 7. W hen a = 5, the inequality is false. W hen <2 = 6 and when a = 7,
the inequality is true. So Mallory says th a t th e solution is a > 6. Is h er reasoning
correct? Justify your answer,
b. Reasoning Explain w hy substituting values into th e inequality does n o t
guarantee th a t Mallory’s solution is correct. - Geom et ry Suppose a triangle has side lengths a, b, an d c, w here c is th e length of
th e longest side. You can use th e following eq u a tio n an d inequalities to determ ine
w hether th e triangle is right, acute, or obtuse.
- If a2 + b2 = c2, th e n th e triangle is right.
- If a2 + b2 > c2, th e n th e triangle is acute.
- If a2 + b2 < c2, th e n th e triangle is obtuse.
Classify each triangle w ith th e following side lengths as right, acute, or obtuse.
a. 4 in., 5 in., 6 in. b. 3 cm, 4 cm, 5 cm c. 10 m, 15 m, 20 m
176 Chapter 3 Solving Inequalities