Section 4.2 Solving Linear Inequalities Using the Multiplication-Division Principle.

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Presentation transcript:

Section 4.2 Solving Linear Inequalities Using the Multiplication-Division Principle

4.2 Lecture Guide: Solving Linear Inequalities Using the Multiplication-Division Principle Objective 1: Solve linear inequalities using the multiplication-division principle for inequalities.

Verbally Order Preserving: If ____________ sides of an inequality are multiplied or ____________ by a positive number, the result is an inequality that has the same ____________ as the original inequality. Algebraically If a, b, and c, are real numbers then, then is __________to. Numerical Examples is equivalent to And to. Multiplication-Division Principle for Inequalities:

Verbally Order Reversing: If ____________ sides of an inequality are multiplied or divided by a negative number and the order of inequality is ____________, the result is an inequality that has the ____________ solution as the original inequality. Algebraically If a, b, and c, are real numbers then, then is equivalent to. Numerical Examples is equivalent to and to. Multiplication-Division Principle for Inequalities:

Use the multiplication-division principle of equality to solve each inequality. 2.1.

Use the multiplication-division principle of equality to solve each inequality. 4.3.

Use the multiplication-division principle of equality to solve each inequality. 6.5.

Use the multiplication-division principle of equality to solve each inequality. 7.

Use the multiplication-division principle of equality to solve each inequality. 8.

Use the multiplication-division principle of equality to solve each inequality. 9.

Use the multiplication-division principle of equality to solve each inequality. 10.

5−911 6−69 7− −1 11. Use the table to solve each equation or inequality. (a) (b) (c)

12. Use the graph to solve each equation or inequality. (a) (b) (c)

13. A high school band is having a fund raiser to raise money for a trip. The cost of renting a snow-cone machine for the fundraiser includes a fixed cost of $84 plus a variable cost of $0.30 per snow-cone. Snow-cones can be sold for $1.50 each. (a) Write an equation for the cost of renting the machine and selling x snow-cones. (b) Write an equation for the revenue generated by selling x snow-cones.

13. A high school band is having a fund raiser to raise money for a trip. The cost of renting a snow-cone machine for the fundraiser includes a fixed cost of $84 plus a variable cost of $0.30 per snow-cone. Snow-cones can be sold for $1.50 each. (c) Determine the values of x for which. (d) Interpret the meaning of the answer to part (c).