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Copyright © Swun MathCopyright © Swun Math Grade 8 Unit 4 Lesson 8 P TE

Homework

Unit 4 · Lesson 8: Equations with Rational Numbers

Objective: I will solve equations with rational number coefficients and constants.

Vocabulary Steps:

Expression Equation Variable

ퟓퟓퟓퟓ풙풙ퟓퟓ−ퟗퟗ풙풙+ퟑퟑퟑퟑ=ퟕퟕ풎풎+ퟖퟖퟓퟓ

Term Coefficient Constant

Fractions:

1. Determine the LCD (least common
   denominator).


2. Multiply both sides by the LCD.


3. Use inverse operations to solve.

Decimals:

1. Determine the power of 10 that will clear the
   decimal.


2. Multiply both sides by the power of 10.


3. Use inverse operations to solve.
   
   
   1. Collect like terms.
   
   
   2. Isolate the variable.
   
   
   3. Solve the equation.
   
   
   4. Check by inserting the answer into the
      equation.
   
   
   
   

Example # 1 Example # 2

Directions Solve for the given variable.

�

2

3

푦푦+

1

2

푦푦�=�

5

6

• 2푦푦�

Solution:

I will distribute the number 6 to the equation to clear the

fractions.

6 �

2

3 푦푦+

1

2 푦푦�= 6�

5

6 + 2푦푦�^

4 푦푦+ 3푦푦= 5 + 12 푦푦

7 푦푦= 5 + 12 푦푦

− 7 푦푦 − 7 푦푦

0 = 5 + 5푦푦

0 = 5 + 5푦푦

− 5 − 5

−5 = 5푦푦

푦푦=− 1

4. 6 푥푥+ 6 = 7. 2 푥푥+ 1. 2

Solution:

I used the number 10 to remove the decimals.

10(4.6푥푥+ 6.8) =10(7.4푥푥+ 1.2)

46 푥푥+ 68 = 74 푥푥+ 12

− 46 푥푥 − 46 푥푥

68 = 28 푥푥+ 12

68 = 28 푥푥+ 12

− 12 − 12

56 = 28 푥푥

56

28 =

28 푥푥

28

2 =푥푥

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