Solving inequalities annotated
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This document discusses how to solve inequalities by treating them as equalities and then determining the set of numbers that make the inequality true. It explains that the solution to an inequality is a set or interval expressed visually by graphing. Examples are provided to demonstrate solving different types of inequalities algebraically and checking solutions by plugging numbers into the original inequality. The document also notes that the direction of the inequality sign must be changed when multiplying or dividing by a negative number.
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Solving inequalities annotated
- 1. Solving Inequalities Sections 5.1 & 5.2 page 285-297
- 2. You already know > ≥ < ≤ Greater than Greater than or equal to Less than Less than or equal to
- 3. But what does that mean? Inequality is a comparison The solution is a set of numbers More than just one thing in the solution Express as a set or an interval Visual solution – graph the set
- 4. What numbers make the inequality true? How do we express all the numbers that will work? 𝑥 > 5 graphical interval set (5, ∞) {𝑥|𝑥 > 5} 5
- 5. Solve the Inequality Pretend like the inequality is an equal sign and solve. Graph the solution set. Check your answers. 𝑥 − 3 > 7 +3 +3 𝑥 > 10 10 Pick a number in the solution set. 𝑙𝑒𝑡 𝑥 = 11 Plug it in and see if it works 11−3 > 7 8 > 7
- 6. 3𝑥 − 1 ≤ 11 Example: Solve the inequality and graph the solutions set.
- 7. When you change the sign you must change the sign. Multiply or divide across the inequality with a negative you must flip the inequality. You are changing the sign of the number so you must change the sign of the inequality to keep it true. 7 < 9 7 −2 9(−2) −14 − 18> Direction of the Inequality Changed
- 8. Example: Solve the inequality and graph the solution set. − 𝑐 6 ≥ 7
- 9. Example: Solve the inequality and graph the solution set. −28 ≤ −6𝑥
- 10. Example: Solve the inequality and graph the solution set. − 3 4 𝑟 ≤ −6
- 11. Homework Page 288 #12-29 Page 295 #12-29