PP Section 2.3

# PP Section 2.3 - Solving Inequalities 7 1 2x inequality the...

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Inequalities – Part 1

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Definition An inequality is an algebraic expression  involving one of the fours signs:  < , , , Examples: 8 2 < 3 - x 4 3 ) 1 ( 2 + - - x x 5 4 2 + x
Solving Inequalities To solve an inequality means to find all the real  numbers that satisfy the inequality. An inequality is solved by creating equivalent  inequalities. Equivalent inequalities are created using  the properties of inequalities.

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Properties of Inequalities For real numbers a, b, and c: 1.   If a < b, then a + c < b + c. 2.   If a < b and c is positive, then ac < bc. 3.  If a < b and c is negative, then ac > bc. 4.  If a < b and b < c, then a < c. Note:  the four properties above could have been  written with any of the other three signs.

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Unformatted text preview: Solving Inequalities 7 1 2x inequality the Solve &lt; + Using interval notation: (-, 3) Graphically: 3 6 2 7 1 2 &lt; &lt; &lt; + x x x Solving Inequalities x x 2 1 5 ) 2 ( 4 inequality the Solve + +--x x 2 1 5 8 4 + + +-12 6 2 1 13 4-- + +-x x x 2 x Solving Inequalities 2 1 1 3 3 4 1 inequality the Solve &lt; + x 4 3 1 3 2 2 1 1 3 3 4 1 + &lt; &lt; + x x 12 1 3x 6 + &lt; 11 3x 5 &lt; 3 11 3 5 &lt; x Solving Inequalities 4 5 2 inequality the Solve &lt;-x 4 5 2 4 &lt;-&lt;-x &lt; &lt; 2 9 , 2 1 OR 2 9 2 1 x 9 2 1 &lt; &lt; x Solving Inequalities 4 5 2 inequality the Solve -x 4 5 2 OR 4 5 2---x x 1 2 OR 9 2 x x 2 1 OR 2 9 x x...
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## PP Section 2.3 - Solving Inequalities 7 1 2x inequality the...

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