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Thinking
Mathematically
Algebra: Equations and
Inequalities
6.4 Linear Inequalities in One Variable
Inequalities
• Solving – finding the set of numbers that
satisfy the inequality.
• English phrases:
–
–
–
–
–
At least
At most
Is between
Is no more than
Is no less than
Graphing Inequalities
Inequalities can be graphed on a number line by
marking all of the points on the line that correspond
to numbers that will make the inequality a true
statement.
•An open circle indicates that a point is not part of
the solution
•A closed circle indicates that a point is part of the
solution
Examples: Graphing Inequalities
Exercise Set 6.4 #3, #9
x  4
2 x 5
Solving Linear Inequalities
The procedure for solving linear inequalities
is the same as the procedure for solving linear
equations, with one important exception:
When multiplying or dividing both sides of
the inequality by a negative number, reverse
the direction of the inequality symbol,
changing the sense of the inequality.
Examples: Solving Linear
Inequalities
Exercise Set 6.5 #33, #49, #61
 3x  15
2 x  5  5 x  11
3  x  2 1
Thinking
Mathematically
Algebra: Equations and
Inequalities
6.4 Linear Inequalities in One Variable