Page 680 - Algebra 1

Check Verifythatthesolutionsarenotextraneous.
Math Reasoning
Justify Why do you have to check both solutions to the equation?
11 + 9 _ _
2+9 _ _
x-1= x+9;x=11 x- 2 2x - 4
or Substitute. Simplify.
x-1= x+9;x=2 x - 2 2x - 4
11 - 1
11 - 2 2(11) - 4
2-1
2 - 2 2(2) - 4
10 10
_9 = _9 ✓
_1 _11
0 = 0 ✗
2 is an extraneous solution.
The solution is x = 11.
Application: Painting
Example
5
It takes Samuel 7 hours to paint a house. It takes Jake 5 hours to paint the same house. How long will it take them if they work together?
SOLUTION
Understand The answer will be the number of hours h it takes for Samuel and Jake to paint the house.
Samuel can paint the house in 7 hours, so he can paint _1 of the house
per hour.
7
Jake can paint the house in 5 hours, so he can paint _1 of the house per hour. 5
Plan The part of the house Samuel paints plus the part of the house Jake paints equals the complete job. Samuel’s rate times the number of hours worked plus Jake’s rate times the number of hours worked will give the complete time it will take them to paint the house. Let h represent the number of hours worked.
(Samuel’s rate)h + (Jake’s rate)h = complete job _1h + _1h = 1
Multiply each term by the LCD, 35.
Simplify each term.
Combine like terms; and divide both sides by 12.
Together, they can paint the house in 2_11 hours. 12
75
Solve
_1 h + _1 h = 1 75
(35)_1 h + (35)_1 h = (35)1 75
Math Reasoning
Verify Show that the solution _35 hours
12
satisfies the original
equation.
5h + 7h = 35 _
h = 35 12
Lesson 99 665