Lesson Master 5-6B Page 2

Name Name

5-6B Lesson Master 5-6B page 2

SKILLS Objective C: Solve equations of the form x + a = b In 9–14, solve and graph your solution on the given number line. __3 > x + a < b 9. s + 8.8 < 4.76 s < −4.04 10. t + 12.3 > 9 t −3 and inequalities of the form . 10 In 1 and 2, give the reason for each step of the solution. -4.04 s -3 t + < 1. a. x 3.4 −6.8 Original inequality -5 -4 -3 -2 -1 0 12 -4-5 -3 -2 -1 10

b. x + 3.4 + −3.4 < −6.8 + −3.4 Addition Property of Inequality ≥ ≥ 11. u + −8.01 ≥ −8.01 u 0 12. v + −9.4 ≥ −6.2 v 3.2

c. x < −6.8 + −3.4 Property of Opposites 0 u 3.2 v d. x < −10.2 Addition of negative numbers -1-2 0 12 -1 10 2 3 4 5

__3 2. a. 4 ≤ −5.2 + y Original equation ≤ < 4 13. w + 18.68 ≤ 12.4 w −6.28 14. x + 3 < 8 - 5 x 0 __3 b. 4 + 5.2 ≤ −5.2 + 5.2 + y Addition Property of Inequality -6.28 4 w 0 x __3 -5-6-7 -4 -3 -2 -1 0 1 c. 4 + 5.2 ≤ y Property of Opposites -1-2 0 12 4 15. Multiple choice. Which of the following are solutions to −21.3 + x < 1.3? d. 9.95 ≤ y Addition of positive numbers There may be more than one correct answer. A, B, C, F

In 3–8, solve and graph your solution on the given number line. A −20 B 20 C −22.6 _5 D 22.6 E 40 F −40 __3 < __4 > 3. m + 5 < 9 m 3 8 4. n + 2.8 > 2 n 0 8 5 16. Shyamala will be able to visit an out-of-town friend this summer 5 0 3 n if she saves up some money. The trip will cost at least $150. So far, 8 m -1 10 2 3 4 she has saved $52, and she expects to save $6 each week from her 10-1 2 34 allowance. If the trip will take place 9 weeks from today, how much ≥ ≤ more money will Shyamala need at the time she leaves for the trip? 5. p + −3 ≥ −5 p −2 6. q + −8 ≤ −6 q 2 a. Write an inequality to answer the question.

p 2 = q Sample: Let x money needed. -3-1-2 0123 -1-2 01234 52 + 9 · 6 + x ≥ 150

≥ __1 __1 ≤ > b. Solve your inequality. x 44 7. h + −6 ≤ −6 h 0 8. r + −7.3 > 6.24 r 13.54 8 8 17. John has scores of 98, 88, 95, 85, and 92 on ﬁ ve math tests. His total 0 h 13.54 r number of points for six tests must be at least 546 in order for his -1-2 0 12 0-5 51015 20 average score to be at least 91. What score must he get on the sixth test to achieve his goal?

a. Write an inequality to answer the question. = Sample: Let t the score for the sixth test. 98 + 88 + 95 + 85 + 92 + t ≥ 546

≥ b. Solve your inequality. t 88 Transition Mathematics 227 228 Transition Mathematics

UCSMP_SMP08_NL_TM1_TR1_C05_211-2227 227 5/23/07 11:50:40 AM UCSMP_SMP08_NL_TM1_TR1_C05_211-2228 228 5/23/07 11:50:43 AM

Name Name

Questions on SPUR Objectives 5-7A Lesson Master See pages 352–355 for objectives. 5-7B Lesson Master

REPRESENTATIONS Objective N = - 1. a. Use a fact triangle to solve the equation x - y = −6 for y. y x −6 REPRESENTATIONS Objective N: Graph solutions to equations of the form x + y = k or x - y = k. b. Is the point (−13, −7) on the line of equation x - y = −6? = - 1. a. Use a fact triangle to solve the equation x + y = 1 for y. y 1 x Justify your answer. b. Is the point (16, −15) on the line of equation x + y = 1? Yes; Sample: Tracing along the graph, using a Justify your answer. graphing calculator, yields the point (−13, −7). Yes. Sample: Substituting 16 for x and −15 In 2–7, graph the line with the given equation. for y makes the sentence true. 2. x + y = −2 3. x - y = 4 y y 2. Examine the graph of x + y = 2 in the graph at the right. y 10 10 10 8 8 8 a. Where does the line cross the x-axis? (2, 0) 6 6 6 4 4 4 b. Where does the line cross the y-axis? (0, 2) 2 2 2 x x x 2-2-4-6-8-10 46810 2-2-4-6-8-10 46810 2-2-4-6-8-10 46810 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8 -10 -10 -10

4. y = x + 5 5. x = 9 - y 3. Graph x - y = 8 by following Parts a through e. y y y 10 10 10 8 8 8 = a. If x 0, what is the value of y? −8 6 6 6 4 4 4 b. Write the coordinates in Part a as an ordered pair. 2 2 2 x x x (0, −8) 2-2-4-6-8-10 46810 2-2-4-6-8-10 46810 2-2-4-6-8-10 46810 -2 -2 -2 -4 -4 -4 c. If y = 0, what is the value of x? 8 -6 -6 -6 -8 -8 -8 d. Write the coordinates in Part c as an ordered pair. -10 -10 -10 (8, 0) 6. −3 = x + y 7. −6 + x = 2 - y y y 10 10 e. Graph the two points in Parts b and d, then draw 8 8 a line through the two points. 6 6 4 4 2 2 x

Transition Mathematics 229 230 Transition Mathematics

UCSMP_SMP08_NL_TM1_TR1_C05_211-2229 229 5/23/07 11:50:45 AM UCSMP_SMP08_NL_TM1_TR1_C05_211-2230 230 5/23/07 11:50:47 AM A32 Transition Mathematics

SMP08_NL_TM1_TR_C01-06_A1-A42.inA32 A32 5/24/07 12:40:33 PM