The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 3.7: SOLVING EQUATIONS WITH VARIABLES ON

BOTH SIDES, INCLUDING IDENTITIES AND EQUATIONS THAT

HAVE NO SOLUTION

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When you solve an equation that has a variable on both sides, you may

• Find one solution.


• Obtain a false statement, which means there is no solution.


• Obtain a true statement, which means that the equation is an identity and is true for all
  real numbers.

EXAMPLES

3(x−4)=x+ 6 4 x+ 9 = 1 +4(x+2) 3 x− 7 = 7 + 3 x

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3 x− 12 =x+ 6 4 x+ 9 = 1 + 4 x+ 8 − 7 = 7

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2 x− 12 = 6 4 x+ 9 = 9 + 4 x False statement, no solution

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2 x= 18 9 = 9

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x= 9 True statement, an identity

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One solution

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DIRECTIONS: Solve each equation, if possible, or state if the equation is an identity or if it

has no solution.

1. 4 x+ 1 =7(x−2) 2. 3 x+x= 4 x− 3


2. 2(y+3)= 2 y+ 6 4. 5 x− 7 = 5 x+ 9


3. y+ 9 = 2 y+ 9 6. 2 y− 12 = 2 y


4. x+ 6 =

1

2

(12+ 2 x) 8. −

1

3

(12+ 9 y)= 4 − 3 y

CHALLENGE:Leah solved the equation 3x+ 3 =4(x+2). She found the

solution to bex=1. Was she correct? If her answer was wrong, explain

why and find the correct answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.