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Math Pacing

Solving Multi-Step Inequalities. Math Pacing. Solve each inequality. 1. 2. 3. Which inequality is not represented by the graph:. Solving Multi-Step Inequalities.

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Math Pacing

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  1. Solving Multi-Step Inequalities Math Pacing Solve each inequality. 1. 2. 3. Which inequality is not represented by the graph:

  2. 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. Solving Multi-Step Inequalities

  3. ScienceThe inequality F > 212represents 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 Example 3-1a

  4. Original inequality Subtract 32 from each side. Simplify. Multiply each side by Simplify. Solve a Real-World Problem Example 3-1a Answer: Water will be a gas for all temperatures greater than 100°C.

  5. ScienceThe boiling point of helium is –452°F. Solve the inequality to find the temperatures in degrees Celsius for which helium is a gas. Do this one in your notes, please! Example 3-1b Solve a Real-World Problem Subtract 32 from each side Multiply each side by 5/9 Answer: Helium will be a gas for all temperatures greater than –268.9°C.

  6. Then check your solution. Original inequality Subtract 13 from each side. Simplify. Divide each side by –11 andchange Simplify. Inequality Involving a Negative Coefficient Example 3-2a

  7. Answer: The solution set is Inequality Involving a Negative Coefficient Example 3-2a Check To check the solution, substitute –6, a number less than –6, and a number greater than –6.

  8. Then check your solution. Answer: Do this one in your notes, please! Example 3-2b Inequality Involving a Negative Coefficient Subtract 3 from each side Divide each side by – 8 AND reverse the inequality

  9. Four timesa number plus twelve is less than a numberminus three. 4n + 12 < Write and Solve an Inequality Example 3-3a 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

  10. 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 Example 3-3a

  11. Answer: Write and Solve an Inequality Example 3-3b Write an inequality for the sentence below. Then solve the inequality. 6 times a number is greater than 4 times the number minus 2.

  12. Solving Multi-Step Inequalities When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols. Solving Multi-Step Inequalities

  13. 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 Example 3-4a

  14. Answer: Since is the same as the solution set is Distributive Property Example 3-4a

  15. Answer: Do this one in your notes, please! Example 3-4b Distributive Property Distributive Property Combine like terms Subtract p from each side Add 2 to each side Divide each side by 3

  16. 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. Solving Multi-Step Inequalities

  17. Original inequality Distributive Property Combine like terms. Subtract 4s from each side. This statement is false. Empty Set Example 3-5a Answer: Since the inequality results in a false statement, the solution set is the empty set Ø.

  18. Do this one in your notes, please! Example 3-5b Empty Set Distributive Property Combine like terms This statement is false. Answer: Ø

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