Chapter 7 Lesson 6Solving Multi-Step Inequalities

pgs. 355-359

Chapter 7 Lesson 6Solving Multi-Step Inequalities

pgs. 355-359

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.

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

Example 1: Solve a Two-Step Inequality

Solve 3x + 4 31 and check your solution. Graph the solution on a number line.

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 31Subtract 4 from each side: 3x + 4 -4 31 -4

Simplify: 3x 27 Divide each side by 3: 3x 27

3 3 Simplify: x 9

Check in theoriginal problemusing 7:3(7) + 4 3121 + 4 3125 31

Example 2: Reverse the Inequality Symbol

Example 2: Reverse the Inequality Symbol

Solve -6.1n 3.9n + 5, check your solution and graph the solution on a number line.

Solve -6.1n 3.9n + 5, check your solution and graph the solution on a number line.

Write the inequality: -6.1n 3.9n + 5Subtract 3.9n from each side: -6.1n 3.9n + 5

-3.9n -3.9n

Simplify: -10n 5Reverse the inequality and divide each side by -10: -10n 5 -10 -10

Simplify: n -0.5

Check using-1 in the originalInequality:-6.1(-1) 3.9(-1) + 5 6.1 -3.9 + 56.1 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

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?

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 weightInequaltiy: 3 (10 + c) 213

Write the inequality: 3 (10 + c) 213 Distribute: 30 + 3c 213Sub. 30 from each side: 30 - 30 + 3c 213 - 30

Simplify: 3c 183 Divide each side by 3: 3c 183

3 3 Simplify: c 61

So the contentsShould weigh lessThan 61 pounds

Now you give it a whirl!!Now you give it a whirl!!

A. m + 9 5

2

B. 16 - 4n 20

C. 3x - 2 10 - x

D. 0.5a - 1.4 2.1

A. m + 9 5

2

B. 16 - 4n 20

C. 3x - 2 10 - x

D. 0.5a - 1.4 2.1

Solve, check and graph each inequality m + 9 -9 5 - 9 2 m -4 2 m -8(2) m -4(2) 2 16 -16 - 4n 20 - 16 -4n 4 n -1

3x - 2 + 2 10 + 2 -x3x 12 - x3x + x 12 - x + x4x 12x 3

.5a -1.4 + 1.4 2.1 + 1.4

.5a 3.5 a 7

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

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