Teaching Notes 3.14: Solving Combined
Inequalities—Conjunctions
Solving conjunctions involves rewriting a combined inequality as two separate inequalities,
solving each inequality, and sometimes rewriting the solution. Students may have trouble
applying one or more of these skills.- Explain that a conjunction is a compound mathematical sentence that joins two sentences
with the word ‘‘and.’’ When students solve a conjunction, they find values that make both
statements true. - Review the steps for solving conjunctions and the examples on the worksheet with your stu-
dents.- Discuss the first example on the worksheet. Explain that this statement can be rewritten
as a conjunction. Be sure that your students can rewrite the statement correctly and solve
each inequality. Depending on the abilities of your students, you may find it helpful to
review 3.12: ‘‘Solving Inequalities with Variables on One Side.’’ Note the way the solution
is rewritten as a combined inequality:− 3 <x<3. If necessary, discuss the example step
by step. - Discuss the second example on the worksheet, noting that this statement, too, was
rewritten. Explain that the direction of the inequality symbols must be reversed because
both sides of the inequalities are divided by−2. Also explain the way the solution
was rewritten in the preferred form. If necessary, review 3.13: ‘‘Rewriting Combined
Inequalities as One Inequality.’’
- Discuss the first example on the worksheet. Explain that this statement can be rewritten
EXTRA HELP:
Solutions of conjunctions must make both inequalities true.ANSWER KEY:
(1) 1 <x< 11 (2) 8 <y≤ 9 (3)− 9 ≤y< 1 (4) 1 ≤y< 5 (5)− 3 <x≤ 1
(6)− 3 <y≤ 4 (7)− 1 ≤y< 1 (8) 5 <x< 9
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(Challenge)Serena divided both sides of the inequality by−2 and did not change the direction of
the inequality symbol. The correct answer is− 2 <y<0.
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