Download Sec 4.8 Solving Equations with fractions Add Chapter 4 test # 1

Sec 4.8 Solving Equations with fractions
Add Chapter 4 test # 1-27 p 303 to homework
Test Problem:
Example 1 Solve − 78 k = 21
Notice term containing k is isolated on the left and number term is on the right
To get k multiply both sides of the equation by the reciprocal of − 78 which is − 87
− 87 − 78 k = 21− 87 
sign on the left is +
21
8
reduce
+ 1k = 1 − 7 
3 8
k = −11
k = −24
Test Problem:
Example 3 Solve y − 15
= 321
32
To isolated the y term on the left add the opposite of − 15
which is + 15
to both sides of the
32
32
equation
y − 15
+ 15
= 321 + 15
32
32
32
y + 0 = 16
reduce
32
y = 12
Clearing fractions first
Example 4 Solve x + 16 = 34
Multiply both sides of the equations by the LCD of any fractions in the equation
The LCD of 4 and 6 = 12
12x + 16  = 12 34 
multiply by LCD
1
3
12x + 12 6  = 12 4 
use distributive property
12
12
3
12x + 6 = 1 ⋅ 4
reduce
12x + 2 = 9
notice there are no fractions in the equation
−2 −2
subtract 2 from both sides of the equation
—————————12x
=7
divide both sides by 12, the coefficient of x
x
= 127
p289.
Strategy
Simplify the equations:
1. Clear the equation of fractions
2. Use the distributive property to remove any parentheses
3. Combine like terms on either side of the equation
Isolate the variables:
4. Use the addition and subtraction properties of equality to get the variables on one side
and the constant terms on the other
5. Combine like terms when necessary
6. Undo the operations of multiplication and division to isolate the variable
1
#58 Solve 14 y −
2
3
=
1
2
LCD of 4,3,2 = 12
12 14 y − 23  = 12 12 
multiply both sides by LCD
1
2
1
use the distributive property to simplify
12 4 y − 12 3  = 12 2 
2
3y − 4 1  = 6
reduce
3y − 8 = 6
notice there are no fractions in the equation
+ 8 +8
add 8 to both sides of the equation
—————————3y = 14
divide both sides by 3, the coefficient of y
14
2
y = 3 or y = 4 3
Test Problem:
Example 5 Solve 34 h − 12 = 58 h
Multiply both sides of the equations by the LCD of any fractions in the equation
The LCD of 2,4 and 8 = 8
8 34 h − 12  = 8 58 h
multiply both sides by LCD
3
1
8 5
8 4 h − 8 2  = 1  8 h
use the distributive property to simplify
2 3
4 1
 h − 1  1  = 5h
reduce
1 1
6h − 4 = 5h
notice there are no fractions in the equation
− 6h
− 6h
subtract 6h from both sides of the equation
—————————to put the variable on the right
− 4 = −1h
divide both sides by −1, the coefficient of h
4 = h or h = 4
Do NOW
a. y + 15 = 23
b. 45 p − 12 = 34 p
c. 25 x + 1 = 13 + x
ans. a.
7
15
b.
1
5
c.
10
9
Example 6 and 7 Word problems p 289 and 290
2