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PRE-ALGEBRA

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Lesson 2-9 Warm-Up

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PRE-ALGEBRA “Solving One-Step Inequalities by Adding and Subtracting” (2-9) (3-1) What are “equivalent inequalities”? What is the “Addition Property of Inequality”? Equivalent Inequalities: two inequalities with the same solutions Example: x < 3 has the same solution as x + 4 < 7. As you can see in the picture below, if you take 4 blocks away from both sides of x + 4 7, you get x < 3. Rule: Addition Property of Inequality: If you add the same number to both sides of an inequality, the inequality is equivalent to the original inequality. Note: This property is also true for ≥ and ≤. if a > b, then a + c > b + c if a < b, then a + c < b + c Example: 3 > 1, so 3 + 1 > 1 + 1 Example: -5 < 4, so -5 + 2 < 4 + 2 4 > 2 -3 < 6 Notice the left side is stays 2 bigger than the right side in the example on the left and 9 less than the right side in the example on the right if you add the same amount to both sides of the inequality.

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PRE-ALGEBRA What is the “Subtraction Property of Inequality”? Rule: Subtraction Property of Inequality: If you subtract the same number to both sides of an inequality, the inequality is equivalent to the original inequality. if a > b, then a - c > b - c if a < b, then a - c < b - c Example: 3 > 1, so 3 - 1 > 1 - 1 Example: -5 < 4, so -5 - 2 < 4 - 2 Note: This property is also true for ≥ and ≤. Solving One-Step Inequalities By Adding and Subtracting (2-9)

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PRE-ALGEBRA How do you check to make sure an equality it written or graphed correctly? To check an inequality, replace the variable with one of the solutions of the inequality Example: Solve and graph x – 3 < 5. x – 3 + 3 < 5 + 3 Add 3 to both sides. x < 8Simplify Check (Step 1): Both sides of the inequality should be equal when you substitute the variable with the solution. 8 – 3 = 5 Substitute or “Plug In” 8 for x. 5 = 5 (True Statement)Simplify Check (Step 2): Check to make sure the inequality symbol in pointing the correct way by substituting the variable with an solution. 7 – 3 < 5 7 is one of the solutions for x < 8. 4 < 5 (True Statement) Simplify “Solving One-Step Inequalities by Adding and Subtracting” (2-9)

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PRE-ALGEBRA Solve p –3 < –5. p – 3 < – 5 Add 3 to both sides to isolate the variable + 3 + 3 Step 1: Check whether your answer is a solution to the related equation. Check: p – 3 = – 5 Write the related equation. – 5 = – 5 Substitute –2 for p. (–2) – 3 – 5 Solving One-Step Inequalities by Adding and Subtracting LESSON 2-9 Additional Examples p < – 2 Simplify. + 0

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PRE-ALGEBRA (continued) Substitute a number less than –2 for p. (–3) – 3 < – 5 Step 2: Check the inequality symbol by substituting into the inequality. p – 3 < – 5 – 6 < – 5 LESSON 2-9 Additional Examples Solving One-Step Inequalities by Adding and Subtracting

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PRE-ALGEBRA Solve each inequality. Graph the solutions. a. b. 4 + s – 4 < 12 – 4 Subtract 4 from each side. 4 + s < 12 s < 8 Simplify. 4 + s < 12 –16 y – 14 > – > – –16 + 14 y – 14 + 14 Add 14 to each side. > – –2 y or y –2 Simplify. (Switch the sign if you switch the sign around). > – < – Solving One-Step Inequalities by Adding and Subtracting LESSON 2-9 Additional Examples

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PRE-ALGEBRA Solve 8 d – 2. Graph and check your solution. > + 2 + 2Add 2 to each side. 10 d, or d 10Simplify (Switch the sign if you switch the sign around). > < Check: 8 = d – 2Check the computation. 8 (10) – 2Substitute 10 for d. 8 = 8 8 ≥ d – 2 Check the direction of the inequality. 8 ≥ (9) – 2 Substitute 9 for d. 8 ≥ 7 LESSON 2-9 Additional Examples 8 d – 2 > + 0 Solving One-Step Inequalities by Addition and Subtraction

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PRE-ALGEBRA Suppose your computer’s hard drive has a capacity of 6 gigabytes (GB). The files you have stored on the hard drive occupy at least 2 GB. How much storage space is left for other files? =storage space available.sLet storage space for our files Words is less than or equal to plus total space storage space left Inequality2s6+ < – 2 + s 6 < – – 2 – 2 Subtract 2 from each side to isolate the variable, s. s 4 Simplify. < – At most 4 GB are left. LESSON 2-9 Additional Examples Solving One-Step Inequalities by Adding and Subtracting 0 +

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PRE-ALGEBRA Solve each inequality. 1.e + 4 14 2.–22 g – 6 3.A number q plus the opposite of 5 is less than or equal to 0. > – < – e 10 < – q 5 < – –16 ≥ g or g ≤ – 16 Lesson Quiz LESSON 2-9 Solving One-Step Inequalities by Adding or Subtracting

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