Name DateWORKSHEET 3.13: REWRITING COMBINED INEQUALITIES AS
ONE INEQUALITY
-------------------------------------------------------------------------------------There are two types of combined inequalities: disjunctions and conjunctions. Disjunctions are
two number sentences joined by ‘‘or.’’ Conjunctions are two number sentences joined by
‘‘and.’’EXAMPLES OF DISJUNCTIONS
- x>^4 orx=^4 ,whichisthesameasx≥^4. This statement includes 4 or all real numbers
that are greater than 4. - x<−^1 orx=−^1 ,whichisthesameasx≤−^1. This statement includes−^1 or all real
numbers that are less than− 1. - x<^3 orx>^4. This statement cannot be expressed as one inequality.
EXAMPLES OF CONJUNCTIONS
-^3 <xandx<^7 ,whichisthesameas^3 <x<^7. This statement includes all real num-
bers that are between 3 and 7. It does not include 3 or 7.
- −^4 ≤xandx<^0 ,whichisthesameas−^4 ≤x<^0. This statement includes−^4 and
all numbers between− 4 and0.Itdoesnotinclude0. - − 1 ≥xandx>− 3 ,whichisthesameas− 1 ≥x>− 3. This statement should be written
as− 3 <x≤− 1 .Itincludes− 1 and all the real numbers between− 3 and− 1. It does
not include− 3.
DIRECTIONS: Write a combined inequality for each of the following. If a statement cannot
be expressed as one inequality, write ‘‘impossible.’’- 3 <yandy< 7 2. − 1 <xorx=− 1
- − 4 <xandx≤ 0 4. x>2andx< 5
- 1 >yandy>− 1 6. − 3 ≥yandy>− 10
- x<4andx≥− 1 8. y>3ory< 1
CHALLENGE:What numbers are described byx<0orx≥0? Explain your
answer.113Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.