Solving Problems Involving Inequalities Chapter 3 Section 3.3

Objective Students will solve problems that involve inequalities

Concept When solving word problems involving inequalities, you set the problems up just like you would when solving an equation. Read the problem Choose a variable Write an inequality Solve the inequality

Concept When working with inequalities, it is important to read both the symbols and the words slowly and carefully. Unlike equations, which involve only one sign, inequalities can contain any of the four inequality symbols. Make sure once you have written your inequality you go back to make sure it makes sense with the wording of the problem.

Example Molly set her car’s trip odometer at zero at the start of her trip home. When the odometer showed that she had driven 16 mi, a highway sign showed her that she was still more than 25 mi from her home. What is the minimum total distance, to the nearest mile, that she will have traveled when she arrives home?

Concept To translate phrases such as “is at least” and “is no less than” or “is at most” and “is no more than” into mathematical terms, you use the symbols < or >. This means that it could be equal to the specific number

Example Mike wants to rent a car for his vacation. The rental costs $125 a week plus $.15 a mile. How far to the nearest mile can Mike travel if he wants to spend at most $200?

Example The width of a rectangular computer screen is 20 cm less than twice the length. The perimeter is at least 53 cm. Find the minimum dimensions, in centimeters, of the screen if each dimension is an integer.

Questions

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