1. Linear Inequalities
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2. A linear inequality has a boundary line that can be
expressed in the form
y = mx + b
The solution to the inequality is the set of all ordered pairs
that makes the inequality true.
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3. Example
Graph 2x + y < 4
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4. 1. Graph inequality like a linear equation.
2. Line becomes boundary line.
­ if > (greater than) boundary line is dashed
because values are not
­ if < (less than) part of solution
­ if (greater than or equal to) boundary line is
solid because values
­ if (less than or equal to) are part of solution
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5. 3. Test a point on each side of the boundary line to determine
the solution area.
4. Shade in the region that represents the solution.
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6. Example
Graph y ­ 3 ≥ 0
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7. Graph the solution of
4x ­ y ≤ 6
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8. System of linear inequalities:
Two types of systems.
1. Intersection of the inequalities ( and )
and
The solution to the system is where the solutions for
each individual inequality overlap
2. Union of the inequalities ( or )
or
The solution to the system could be anywhere
within either solution set of each inequality....
combine their solution sets
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9. and
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10. or
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11. Exercise 27
Questions 1 ­ 11
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