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Real Number Inequality Solutions and Real-World Problems

Learn to solve inequalities involving real numbers and apply them to practical scenarios, such as luggage weight restrictions at airports. Practice graphing solutions and solving real-world problems step by step.

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Real Number Inequality Solutions and Real-World Problems

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  1. ANSWER You can rewrite2 x asx  2. The solutions are all real numbers less than or equal to 2. EXAMPLE 4 Solve an inequality using subtraction Solve 9  x+ 7. Graph your solution. 9x+ 7 Write original inequality. 9– 7 x+ 7 – 7 Subtract 7 from each side. 2 x Simplify.

  2. EXAMPLE 5 Solve a real-world problem LUGGAGE WEIGHTS You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weightsw(in pounds) that you can add to the bag. SOLUTION Write a verbal model. Then write and solve an inequality. 16.8 + w 50

  3. ANSWER You can add no more than33.2pounds. EXAMPLE 5 Solve a real-world problem Write inequality. 16.8 + w 50 16.8 + w –16.8 50 –16.8 Subtract 16.8 from each side. w  33.2 Simplify.

  4. ANSWER y> 0.5 for Examples 4 and 5 GUIDED PRACTICE 7. Solve y+ 5.5 > 6. Graph your solution.

  5. w  20.9 lb ANSWER for Examples 4 and 5 GUIDED PRACTICE 8.WHAT IF?In Example 5, suppose your bag weighs 29.1 pounds. Find the possible weights (in pounds) that you can add to the bag.

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