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Solving Multi-Step Inequalities with Distributive Property

Learn how to solve multi-step inequalities involving more than one operation and the Distributive Property. Practice problems included.

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Solving Multi-Step Inequalities with Distributive Property

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  1. Lesson 6-3 Solving Multi-Step Inequalities

  2. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 3a

  4. Objectives • Solve inequalities involving more than one operation • Solve linear inequalities involving the Distributive Property

  5. Vocabulary • none

  6. Multiplication and Division PoE Properties of Equality (PoE) are based on the concept that as long as you do the same thing to both sides of an equation, then you have not changed anything. • Multiplication PoE • For any numbers a, b, and c, if a = b, then ac = bc • You can multiply both sides of an equation by the same thing without changing the equation • Division PoE • For any numbers a, b, and c with c ≠ 0, if a = b, then a/c = b/c • You can divide both sides of an equation by the same thing without changing the equation • Multiplication and division are reciprocal actions

  7. ScienceThe 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. Example 1

  8. Original inequality Subtract 32 from each side. Simplify. Multiply each side by Simplify. Example 1 cont Answer: Water will be a gas for all temperatures greater than 100°C.

  9. Original inequality Subtract 13 from each side. Simplify. Divide each side by –11 andchange Simplify. Answer: The solution set is Example 2 Solve 13 – 11d≥ 79. Then check your solution. Check To check the solution, substitute –6, a number less than –6, and a number greater than –6.

  10. Four timesa number plus twelve is less than a numberminus three. 4n + 12 < Example 3 Write an inequality for the sentence below. Then solve the inequality. Four times a number plus twelve is less than a number minus three.

  11. 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 Example 3 cont

  12. Answer: The solution set is 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. Example 4

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

  14. Summary & Homework • Summary: • Multi-step inequalities can be solved by undoing the operations • Remember to reverse the inequality sign when multiplying or dividing each side by a negative number • When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols • Homework: • Pg 335 16-38 even

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