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Today’s Lesson Solving One-Step Linear Inequalities Unit 3-Lesson 8 Warm-up Activity Let’s warm up today by writing expressions and equations. Work with a partner to solve the following problems. The sum of a number and –2.3 is 7.82. Let x = a number x + (–2.3) = 7.82 +2.3 +2.3 x = 10.12 to “undo” a negative you must use a positive What you do to one side of the equation, be sure and do to the other. The difference of a number and –2.3 is 7.82. Let x = a number x – (–2.3) = 7.82 x + 2.3 = 7.82 –2.3 –2.3 x = 5.52 minus a negative is a positive to “undo” addition you must subtract What you do to one side of the equation, be sure and do to the other. The product of –2.3 and a number is 7.82. Let x = a number –2.3x = 7.82 –2.3 – 2.3 x = –3.4 to “undo” multiplication you must divide What you do to one side of the equation, be sure and do to the other. The quotient of a number and –2.3 is 7.82. Let x = a number x (– 2.3) –2.3 = 7.82 (– 2.3) to “undo” division you must multiply x = –17.986 What you do to one side of the equation, be sure and do to the other. The product of –2.3 and the sum of a number and 2 is 7.82. Let x = a number –2.3(x + 2) = 7.82 –2.3x – 4.6 = 7.82 + 4.6 + 4.6 –2.3x = 12.42 –2.3 – 2.3 x = –5.4 distribute the –2.3 to “undo” subtraction you must add What you do to one side of the equation, be sure and do to the other. Whole-Class Skills Lesson Today we will be solving one-step linear equations. Each inequality has two choices: true or false. Determine which choice is true for each inequality. Then, read the inequality. 2+x<8 if x = 5 or if x = 10 Determine which choice is true for the inequality. 2+5<8 True for x = 5 2+x<8 –2 –2 x<6 or 2 + 10 < 8 What you do to one side of the inequality, be sure and do to the other. to “undo” addition you must subtract 2+x<8 The sum of 2 and a number is less than 8. True for x = 5. True for x < 6. x – 1.2 > –12 if x = –15 or if x = 10 Determine which choice is true for the inequality. –15 – 1.2 > –12 or 10 – 1.2 > –12 True for x = 10 x – 1.2 > –12 + 1.2 + 1.2 x > –10.8 What you do to one side of the inequality, be sure and do to the other. to “undo” subtraction you must add x – 1.2 > –12 The difference of a number and 1.2 is greater than –12. True for x = 10. True for x > –10.8. –x < 8 if x = –10 or if x = 10 Determine which choice is true for the inequality. –(–10) < 8 10 < 8 –x < 8 –1 –1 x > –8 or –10 < 8 True for x = 10 When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality must be changed. –x < 8 The opposite of a number is less than 8. True for x = 10. True for x > –8. 2x ≥ –8 if x = –10 or if x = 10 Determine which choice is true for the inequality. 2(–10) ≥ –8 –20 ≥ –8 2x ≥ –8 2 2 x ≥ –4 or 2(10) ≥ –8 20 ≥ –8 True for x = 10 2x ≥ –8 Two times a number is greater than –8. True for x = 10. True for x ≥ –4. –2x ≤ 8 if x = –10 or if x = 10 Determine which choice is true for the inequality. –2(–10) ≤ 8 20 ≤ 8 –2x ≤ 8 –2 –2 x ≥ –4 or –2(10) ≤ 8 –20 ≤ 8 True for x = 10 When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality must be changed. –2x ≤ 8 Negative two times a number is less than or equal to 8. True for x = 10. True for x ≥ –4. –2x ≥ –8 if x = –10 or if x = 10 Determine which choice is true for the inequality. –2(–10) ≥ –8 or –2(10) ≥ –8 20 ≥ –8 True for x = –10 When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality must be changed. –20 ≥ –8 –2x ≥ –8 –2 –2 x≤4 –2x ≥ –8 Negative two times a number is greater than or equal to –8. True for x = –10. True for x ≤ 4. x > –1.2 3 3 1 x > –1.2 1 3 3 1 x > –3.6 1 3 Dividing by is the same as 3 multiplying by 1 (the reciprocal). x > –1.2 3 A number divided by 3 is greater than –1.2 x – < 5 5 1 – – x < 1 5 –0.6 –0.6 5 – 1 x > –3 1 5 Dividing by is the same as 5 multiplying by 1 (the reciprocal). When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality must be changed. x – < 5 –0.6 The opposite of a number divided by 5 is less than – 0.6