Chapter 7 Lesson 6 Solving Multi-Step Inequalities pgs What you’ll learn: Solve inequalities that involve more than one operation What you’ll learn: Solve inequalities that involve more than one operation

Nearly 10 million Americans go backpacking each year. According to a fitness magazine, to avoid injury, three times the weight of your backpack and its contents should be less than your body weight.  Write an inequality that represents the relationship between body weight and a safe total backpack and contents weight.  Suppose you weigh 120 pounds and your empty backpack weighs 5 pounds. Write an inequality that represents the maximum weight you can safely carry in the backpack.  Write an inequality that represents the relationship between body weight and a safe total backpack and contents weight.  Suppose you weigh 120 pounds and your empty backpack weighs 5 pounds. Write an inequality that represents the maximum weight you can safely carry in the backpack. 3(p + c)  b 3(5 + c)  120

Example 1: Solve a Two-Step Inequality  Solve 3x + 4  31 and check your solution. Graph the solution on a number line. Some inequalities involve more than one operation. To Solve the inequality, work backward to undo the operations, just like you did in solving multi-step equations. Write the inequality: 3x + 4  31 Subtract 4 from each side: 3x  Simplify: 3x  27 Divide each side by 3: 3x  Simplify: x  9 Check in the original problem using 7: 3(7) + 4    31 

Example 2: Reverse the Inequality Symbol Solve -6.1n  3.9n + 5, check your solution and graph the solution on a number line. Write the inequality: -6.1n  3.9n + 5 Subtract 3.9n from each side: -6.1n  3.9n n -3.9n Simplify: -10n  5 Reverse the inequality and divide each side by -10: -10n  Simplify: n  -0.5 Check using -1 in the original Inequality: -6.1(-1)  3.9(-1)   1.1 

 Remember: DO NOT reverse the inequality sign just because there is a negative sign in the inequality!!!  Only reverse the sign when you multiply or divide by a negative number. (In other words, when the variable is negative).  Remember: DO NOT reverse the inequality sign just because there is a negative sign in the inequality!!!  Only reverse the sign when you multiply or divide by a negative number. (In other words, when the variable is negative).

Example 3: Inequalities with grouping symbols  A person weighing 213 pounds has a 10-pound backpack. Refer to the application on pg. 355 in the text. What is the maximum weight for the contents of the pack? Words: 3 times weight of pack & contents should be less than body weight Inequaltiy: 3 (10 + c)  213 Write the inequality: 3 (10 + c)  213 Distribute: c  213 Sub. 30 from each side: c  Simplify: 3c  183 Divide each side by 3: 3c  Simplify: c  61 So the contents Should weigh less Than 61 pounds

Now you give it a whirl!! A.m + 9  5 2 B n  20 C. 3x - 2  10 - x D. 0.5a  2.1 A.m + 9  5 2 B n  20 C. 3x - 2  10 - x D. 0.5a  2.1 Solve, check and graph each inequality m  m  -4 2 m  -8 (2) m  -4(2) n  n  4 n  -1 3x  x 3x  12 - x 3x + x  12 - x + x 4x  12 x  3.5a  a  3.5 a  7

 Take a look over this tonight. There will be a quiz tomorrow!