from Al Ain to Dubai. But, his car stuck on the highway within 5 km from a mileage marker of 60 km. This means that your friend must be somewhere between 55 km and 65 km. This is an example of an absolute-value inequality. Absolute-value inequality are in one of the two forms: ǀ x – a ǀ < b or ǀ x – a ǀ > b To solve ǀ x – 60 ǀ < 5, we use – 5 < x – 60 < 5 11
2.8.2: Solve an Absolute-Value Inequality For any positive p, if ǀ x ǀ ≤ p, then – p ≤ x ≤ p – p p Examples: Solve the following inequality; then graph the solution set. a) ǀ x – 5 ǀ < 9 b) ǀ 5 – 3x ǀ ≤ 6 12
2.8.2: Solve an Absolute-Value Inequality For any positive p, if ǀ x ǀ ≥ p, then x ≤ – p or x ≥ p – p p Examples: Solve the following inequality; then graph the solution set. a) ǀ x – 7 ǀ > 19 b) ǀ x – 5 ǀ ≥ 18 13
8.3: Systems of Linear Inequalities in Two Variables The solution set of systems of linear inequality is all ordered pairs that satisfy both inequalities. The graph of the solution set of a system of linear inequalities is then the intersection of the graphs of the individual inequalities. Example: Solve the following system of linear inequalities by graphing. x + y > 4 x – y < 2 14
8.3: Systems of Linear Inequalities in Two Variables Solution: We start by graphing each inequality separately. The boundary line is drawn, and using (0, 0) as a test point, we see that we should shade the half-plane above the line in both graphs.
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- Fall '18
- Accounting, Elementary algebra, Negative and non-negative numbers, Binary relation