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Solving & Graphing Inequalities

PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line. LT 2: Solve one-step inequalities. Solving & Graphing Inequalities. Materials Needed Individual Interactive Notebooks Pencil Answer Sheet. You learned that an INEQUALITY compares using symbols:.

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Solving & Graphing Inequalities

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  1. PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line. • LT 2: Solve one-step inequalities. Solving & GraphingInequalities Materials Needed Individual Interactive Notebooks Pencil Answer Sheet

  2. You learned that an INEQUALITY compares using symbols: > 1 Examples from Before > 2 > > • Write the expression from example 1 in words. • Write the expression from example 2 in words.

  3. Comparison Practice • 19 7 • 9 + 8 15 • (9)(4) (12) (3) • 16 ÷ 2 36 ÷ 4 • 17 – 3 21 – 9

  4. You learned that ALBEBRAIC INEQUALITIES contain Variables: b > ½ x ≥ 7 k ≤ 100 5.9 < m Write Your Own Algebraic Inequality f ≤ 13

  5. Now Write 3 more of your ownAlgebraic Inequalities

  6. You learned that a SOLUTION is the answer and makes the inequality TRUE. Example 1 ? 14 21 - 6 14 15 < The solution is 15, This makes the inequality TRUE.

  7. Find the Solution of each Inequality Circle the Solution you found.

  8. You learned that a SOLUTIONS SET is a RANGE of possible answers • It’s like saying: “It’s might be 3, or any number lower than 3.

  9. Use the completed squares to help you fill in the blank ones.

  10. Arrows & Points How to write answers for a SOLUTION SET? For ‘less than’, the arrow points down When there is not an equals line, the point is open. f < 2 For ‘more than’, the arrow points up When there is an equals line, the point is closed. f≥ 2

  11. Practice Which direction does the arrow go? 2) Is the point open or closed? Remember! Graph the solution set for each inequality.

  12. Now that you have reviewed how to graph INEQUALITIES, you will learn to SOLVE them.

  13. Solving for Inequalities is EXACTLY like EQUATIONS. Subtract 6 From both Sides. Bring down what’s left. No equals line open point Q: Why don’t we graph the equation? A: We know the answer, it’s 4. Q: Why do we graph the inequality? A: To show all possible answers. We’re not sure exactly, but we know it’s lower than 4.

  14. Inequalities Equations How are they the Same? Compare Equalities and Inequalities using the Venn Diagram.

  15. Example 1 Example 2 a + 3 ≤5 ─ 3 18 ≥ 6w a ≤ ≥ w 1. To solve, fill in the boxes above. 2. Insert an arrow going in the correct direction below. 1. To solve, fill in the boxes above. 2. Insert the appropriate open or closed point below.

  16. Example 3 Example 4 k ─ 0 < 0 ( ( ) ) k < > 1. To solve, fill in the boxes above. 2. Write the SOLUTION SET FOR example 4 below. 1. To solve, fill in the boxes above. 2. Write the SOLUTION SET FOR example 3 below. w 3 > 4

  17. Practice > 4

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