Transcript Slide 1
Solving Multi-Step Inequalities Solve each inequality. 1. 9v 108 v | v 12 2. 2c 5 3 9 5 c | c 6 3. Which inequality is not represented by the graph: Solving Multi-Step Inequalities Solving inequalities involving more than one operation can be solved by undoing the operations in the same way you would solve an equation with more than one step. Solve a Real-World Problem Science The inequality F > 212 represents the temperatures in degrees Fahrenheit for which water is a gas (steam). Similarly, the inequality represents the temperatures in degrees Celsius for which water is a gas. Find the temperature in degrees Celsius for which water is a gas. Solve a Real-World Problem Original inequality Subtract 32 from each side. Simplify. Multiply each side by Simplify. Answer: Water will be a gas for all temperatures greater than 100°C. Do this one in your notes, please! Solve a Real-World Problem Science The boiling point of helium is –452°F. Solve the inequality to find the temperatures in degrees Celsius for which helium is a gas. 9 C 484 Subtract 32 from each side 5 5 C 9 484 Multiply each side by 5/9 Answer: Helium will be a gas for all temperatures greater than –268.9°C. Inequality Involving a Negative Coefficient Then check your solution. Original inequality Subtract 13 from each side. Simplify. Divide each side by –11 and change Simplify. Inequality Involving a Negative Coefficient Check To check the solution, substitute –6, a number less than –6, and a number greater than –6. Answer: The solution set is Do this one in your notes, please! Inequality Involving a Negative Coefficient Then check your solution. 8 y 8 y 1 Answer: Subtract 3 from each side Divide each side by – 8 AND reverse the inequality Write and Solve an Inequality Write an inequality for the sentence below. Then solve the inequality. Four times a number plus twelve is less than a number minus three. Let n = a number Four times a number plus twelve is less than 4n + 12 < a number minus three. Write and Solve an Inequality Original inequality Subtract n from each side. Simplify. Subtract 12 from each side. Simplify. Divide each side by 3. Simplify. Answer: The solution set is Write and Solve an Inequality Write an inequality for the sentence below. Then solve the inequality. 6 times a number is greater than 4 times the number minus 2. Answer: Solving Multi-Step Inequalities When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols. Distributive Property Original inequality Distributive Property Combine like terms. Add c to each side. Simplify. Subtract 6 from each side. Simplify. Divide each side by 4. Simplify. Distributive Property Answer: Since is the same as the solution set is Do this one in your notes, please! Distributive Property 3 p 2 p 8 p 2 3 p Distributive Property p 8 4p 2 Combine like terms 8 3p 2 Subtract p from each side 10 3 p Add 2 to each side Answer: Divide each side by 3 Solving Multi-Step Inequalities If solving an inequality results in a statement that is always true, the solution is all real numbers. If solving an inequality results in a statement that is never true, the solution is the empty set . The empty set has no members. Empty Set Original inequality Distributive Property Combine like terms. Subtract 4s from each side. This statement is false. Answer: Since the inequality results in a false statement, the solution set is the empty set Ø. Do this one in your notes, please! Empty Set 4r 6 2r 7r 8 5r Distributive Property 2r 6 2r 8 Combine like terms 6 8 This statement is false. Answer: Ø