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

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WORKSHEET 3.15: SOLVING COMBINED

INEQUALITIES — DISJUNCTIONS

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Two inequalities combined by the word ‘‘or’’ are called a disjunction. To solve a disjunction,

follow the steps below:

1. Write two separate inequalities.


2. Solve each inequality.


3. The solution of the disjunction is the solution to either of the inequalities.


4. Check the solution by substituting the value in the original inequality. If the solution is
   correct, it is a solution to either one of the inequalities.

EXAMPLE

Solve 3 x− 2 > 7 or− 2 x− 8 > 2.

3 x− 2 >7or− 2 x− 8 > 2

3 x>9or − 2 x> 10

x>3or x<− 5

The solution is all real numbers that are greater than 3 or less than− 5.

DIRECTIONS: Solve each disjunction.

1. y+ 2 ≤−1ory+ 2 ≥ 3 2.x+ 1 <3orx− 4 > 10


2. y+ 5 ≤−4ory+ 5 ≥ 4 4. 2 x<8or2x> 16


3. − 2 x>10 or 4x> 16 6. 3 x+ 1 ≤4or2x− 3 > 7


4. x− 3 >6orx+ 12 < 9 8. 3 x<15 or 14< 2 x


5. − 3 x+ 1 >10 or 2x+ 1 > 11

CHALLENGE:Eva’s solution to the disjunction 15> 4 x−1or1< 4 x−15 is

x=4. Is she correct? Explain your answer. If she is incorrect, provide the

correct answer.

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