Lesson 5­7
Problem Solving Skills: Work Backwards
Work Backwards ­ start at the end of a problem and work in the reverse direction
Expl:
Expl 1. Jarret purchased a $925 clarinet using his $6.20/h earnings as a cashier. While he was saving, his uncle donated $150 toward his goal. How many hours did Jarret work to earn enough money to buy the clarinet?
Mar 3­10:56 AM
1
Extra 1. Alexandra was standing on the middle step of a staircase, painting a wall. She went up four steps to touch up a spot, then she went down five steps to continue painting. When she had finished everything within reach, she went down six steps to the first step.
a.
Which step is the middle step of this staircase?
b.
How many steps are there in all?
Mar 3­11:00 AM
2
Extra 2. Marsha had some math exercises to do for homework. She did one­half during study period and two­thirds of those remaining while waiting for her friend after school. She had three to finish at home that evening. How many exercises did she have to do for homework?
Mar 3­11:03 AM
3
Lesson 5­8
Graph Open Sentences
Inequality ­ a mathematical sentence that contains one of the symbols <, >, <, >
Expl:
< ­ > ­ < ­ > ­
Solution of an open sentence ­ a value of the variable that makes the equation or inequality true
Expl:
Mar 3­11:06 AM
4
To graph the solutions of an inequality:
1.
Graph the number on a number line
2.
Use an open dot for is greater than (>) and is less than (<) and a solid dot for the equal toos (> ,<)
3.
The arrow points the direction of the symbol. (Make sure the variable is on the left hand side.)
Graph:
a.
x > ­2
b.
m < 5
c.
3 > z
Mar 3­11:09 AM
5
Expl 1. Solve the equation and graph the solution. Use a dot for an equal sign.
m + 9 = 14
Extra 1. For which of the equations that follow does the graph below show the solution?
­2 ­1 0 1 2
A.
2(x + 4) = 10
C. 2(x ­ 4) = 10
B.
2(x + 2) = 0
D. 2(x ­ 2) = 0
Mar 3­11:15 AM
6
Expl 2. Graph each inequailty.
a.
p > ­2
b.
k < 4
Extra 2. For which of the inequalities that follow does the graph below show the solutions?
­5
A.
x < ­4
C. x < ­4
­4
­3
­2
B.
­1
0
1
2
3
4
5
x > ­4
D. x > ­4
Mar 3­11:20 AM
7
Expl 3. Every frame in the store is priced under $35. Write an inequality to describe the situation. Name three possible frame prices.
Extra 3. As required by law, the Promenade Diner displays a sign stating "Maximum Occupancy: 139 persons."
a.
Write an inequality for the situation.
b.
According to the rule, is it legal for 139 people to be in the diner?
Mar 3­11:22 AM
8
Homework
Lesson 5-7 & 5-8
Pg. 244 2-80 Evens
Mar 3­11:25 AM
9