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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 < 6 divide both sides by -3 -3 x /-3 > 6/-3 x > -2. -2.

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solving inequalities
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

solving inequalities1

-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 ≥.

solving inequalities2

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
  • 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.
solve 2 x 4 12
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
solve 2 4 x 10

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