Solving Inequalities

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# Solving Inequalities - PowerPoint PPT Presentation

Solving Inequalities. To solve an inequality, use the same procedure as solving an equation with one exception. When multiplying or dividing by a negative number , reverse the direction of the inequality sign. -3 x &lt; 6 divide both sides by -3 -3 x /-3 &gt; 6/-3 x &gt; -2. -2.

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## PowerPoint Slideshow about 'Solving Inequalities' - twila

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Presentation Transcript
Solving Inequalities
• To solve an inequality, use the same procedure as solving an equation with one exception.When multiplying or dividing by a negative number, reverse the direction of the inequality sign.
• -3x < 6divide both sides by -3

-3x/-3 > 6/-3

x> -2

-2

-1

0

Solving Inequalities
• -4x + 2 > 10

-4x > 8

x < -2

• To graph the solution set, circle the boundary and shade according to the inequality.
• Use an open circle for < or > and closed circles for

≤ or ≥.

0

1

2

Solving Inequalities
• 3b - 2(b - 5) < 2(b + 4)

3b - 2b + 10 < 2b + 8

b + 10 < 2b + 8

-b + 10 < 8

-b < -2

b > 2

Solving Absolute Value Inequalities
• Solving absolute value inequalities is a combination of solving absolute value equations and inequalities.
• Rewrite the absolute value inequality.
• For the first equation, all you have to do is drop the absolute value bars.
• For the second equation, you have to negate the right side of the inequality and reverse the inequality sign.
2x + 4 > 12 or 2x + 4 < -12

2x > 8 2x < -16

x > 4 or x < -8

x < -8 or x > 4

4

-8

0

Solve: |2x + 4| > 12

9

-1

0

Solve: 2|4 - x| < 10

|4 - x| < 5

4 - x < 5 and 4 - x> -5

- x < 1 - x > -9

x > -1 and x < 9

-1 < x < 9