appendix a.6 solving inequalities. introduction solve an inequality finding all values of x for…
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Properties of InequalitiesTRANSCRIPT
Appendix A.6
Solving Inequalities
Introduction Solve an inequality
Finding all values of x for which the inequality is true.
The set of all real numbers that are solutions of an inequality is the solution set of the equality
The set of all points on the real number line that represent the solution set is the graph of the inequality.
Properties of Inequalities
Linear Inequalities
The simplest type of inequality is a linear inequality in one variable.
2x + 3 < 4 3x – 3 > x + 7
Example 2 Solving Linear Inequalities
4x2x31.b
9x37x5.a
Solve each inequality
Solution
8x16x297x2
9x37x5.a
The solution set is all real numbers that are greater than 8,which is denoted by (8 , ∞)
2x10x58x52
8x2x32
4x2x31.b
The solution set is all real numbers that are less than or equal to 2,which is denoted by ( -∞ , 2]
Inequalities Involving Absolute Values