1. Algebra 1
Section 2.8

2. Possible Color Choices for this slide:

3. Equations with Fractions
To eliminate fractions from an algebraic equation, you can multiply both sides of the equation by the least common multiple of the denominators.

4. Solving Equations Containing Fractions
Find the LCD.
Eliminate fractions by multiplying both sides by the LCD.
Solve the resulting equation.
Check the solution.

5. ( ) Example 1 Solve + x – = 3. x 4 1 3 12 + 12(x) – 12 = 12(3) x 4 1 3
( )
(x) – = 12(3) x 4 1 3
The LCD is 12.
3x + 12x – 4 = 36

6. ( ) ( ) Example 2 Solve – = . x + 2 6 x – 1 3 1 9 18 – 18 = 18 x + 2 6
( )
– = 18
( )
x + 2 6
x – 1 3 1 9
The LCD is 18.
3(x + 2) – 6(x – 1) = 2
3x + 6 – 6x + 6 = 2

7. Example 3 The width of the field is one- third of the length.
Let x = the length of the field
Let ⅓x = the width of the field

8. Example 3
The perimeter of the field is found by adding all the lengths of its sides.
P = l + l + w + w 1 3
x + x x x = 280

9. ( ) Example 3 1 3 x + x + x + x = 280 3x + 3x + 3 x + 3 x = 3(280) 1 3
( )
3x + 3x x x = 3(280) 1 3
The LCD is 3.
3x + 3x + x + x = 840
8x = 840

10. Example 3 8x = 840 x = 105 1 x = 35 3 The length is 105 ft.
The width is 35 ft.

11. Solving Equations Containing Decimals
In these equations, you can multiply both sides of the equation by a power of ten.

12. Coins Coin Value Number Value Pennies Nickels Dimes Quarters $0.01
$0.05
$0.10
$0.25
Number p n d q
Value
0.01p
0.05n
0.10d
0.25q

13. Example 5 q 0.25q 17 – q 0.10(17 – q) 0.25q + 0.10(17 – q) = 2.45
Number of coins
Value of coins
Coin
Quarters q
0.25q
Dimes
17 – q
0.10(17 – q)
0.25q (17 – q) = 2.45

14. Solving Coin Problems
1. Read. Find the main unknown and assign a variable to it; then express any other unknowns in terms of it.

15. Solving Coin Problems
2. Plan and organize by making a table indicating the number and the total value of each type of coin.

16. Solving Coin Problems
3. Solve an equation obtained by using the information in the value column and any other information from the problem.

17. Solving Coin Problems
4. Check that you have answered all the questions and that your answers are reasonable.

18. Example 6 n + 4 0.25(n + 4) 2n 0.10(2n) n 0.05n 3n + 5 0.01(3n + 5)
Number of coins
Value of coins
Coin
Quarters
n + 4
0.25(n + 4)
Dimes 2n
0.10(2n)
Nickels n
0.05n
Pennies
3n + 5
0.01(3n + 5)

19. Example 6 n = 40 0.25(n + 4) + 0.10(2n) + 0.05n + 0.01(3n + 5) = 22.25
44 quarters
40 nickels
80 dimes
125 pennies

20. Homework: pp