Page 7 - Demo

Inequalities can be found in daily life. For example, the speed limit on a highway can be thought of as an inequality. Travelers must drive at a speed less than or equal to the speed limit. Just as with equations, there exist advanced or complex inequalities. Advanced inequalities can be solved using inverse operations.MULTI-STEP INEQUALITIESWhen solving inequalities that require multiple steps, remember that multiplying or dividing by a negative value at any point in the solving process will change the direction of the inequality sign. Example 1: Solve and graph the inequality %u20132p %u2013 7 %u2264 8p + 13. %u20132p %u2013 7 %u2264 8p + 13%u20132p %u2013 7 + 7 %u2264 8p + 13 + 7 %u20132p %u2264 8p + 20 %u20132p %u2013 8p %u2264 8p + 20 %u2013 8p %u201310p %u2264 20 10 10%u221210p 20%u2212%u2264%u2212 p %u2265 %u20132 Example 2: Solve and graph the inequality 4 18 123t %u2212 > . 4 18 123t %u2212 > Multiply both sides by 3 to eliminate the fraction.3 4 18 3 123t %u2212 %u2022 %u2022 > 4t %u2013 18 > 36 Solve for t.4t %u2013 18 + 18 > 36 + 18 4t > 54 4 44 4t > 5 t > 13.5LESSON OVERVIEWPerform inverse operations to get all terms with variables on one side.Dividing by a negative value switches the direction of the inequality sign.Remember:A solid dot is used for the %u2264 and %u2265 symbols.Remember:Any point in the shaded region is a solution to the inequality.%u00a9 GOOD AND BEAUTIFUL 3 LESSON 91