Holt CA Course Solving Inequalities by Multiplying or Dividing Preview of Grade 7 AF4.0 Students solve simple linear equations and inequalities over the rational numbers. California Standards
Holt CA Course Solving Inequalities by Multiplying or Dividing When you multiply or divide both sides of an inequality by the same positive number, the statement will still be true. However, when you multiply or divide both sides by the same negative number, you need to reverse the direction of the inequality symbol for the statement to be true.
Holt CA Course Solving Inequalities by Multiplying or Dividing 2 < 4 –4 (1)2 (1)4 > –2 > –4 –2 2 is less than 4. Multiply both sides by –1. Use the number line to determine the correct inequality symbol. Reverse the inequality symbol because –2 is greater than –4. –4 –
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Additional Example 1: Solving Inequalities by Multiplying c4c4 A. ≤ –4 c4c4 ≤ –4 c4c4 ≤ (–4)(4) c ≤ –16 Multiply both sides by 4.
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Additional Example 1: Solving Inequalities by Multiplying t B. > 0.3 t –4 > 0.3 t < (–4)0.3 (–4) t < –1.2 –4 Multiply both sides by –4 and reverse the inequality symbol.
Holt CA Course Solving Inequalities by Multiplying or Dividing Check Additional Example 1B Continued t B. > 0.3 –4 –2 is less than –1.2 Substitute –2 for t. 22 –4 > 0.3 ? 0.5 > 0.3
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. n6n6 A. ≤ –5 n6n6 ≤ –5 n6n6 ≤ (–5)(6) n ≤ –30 Multiply both sides by 6. Check It Out! Example 1
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. r B. > 0.9 r –3 > 0.9 r < (–3)0.9 (–3) r < –2.7 –3 Multiply both sides by –3 and reverse the inequality symbol. Check It Out! Example 1
Holt CA Course Solving Inequalities by Multiplying or Dividing Check Check It Out! 1B Continued r B. > 0.9 –3 –3 is less than –2.7 Substitute –3 for r. 33 –3 > 0.9 ? 1 > 0.9
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Check your answer. Additional Example 2: Solving Inequalities by Dividing A. 5a ≥ 23 5a ≥ a ≥ 23 5 Divide both sides by 5., or Check 5a ≥ 23 5(5) 23 ≥ ? ≥ ? 5 is greater than Substitute 5 for a.
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Check your answer. Additional Example 2: Solving Inequalities by Dividing B. 192< –24b 192 > – 24b –24 – 8 > b Divide both sides by –24, and reverse the inequality symbol. Check 192 < 24b 192 < 24(–10) ? ? 192 < 240 –10 is less than –8. Substitute –10 for b.
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Check your answer. A. 6b ≥ 25 6b ≥ b ≥ 25 6 Divide both sides by 6., or Check 6b ≥ 25 6(6) 25 ≥ ? ≥ ? 6 is greater than Substitute 6 for b. Check It Out! Example 2
Holt CA Course Solving Inequalities by Multiplying or Dividing Solve. Check your answer. Check It Out! Example 2 B. 85 < –17b 85 > –17b –17 –5 > b Divide both sides by –17, and reverse the inequality symbol. Check 85 < –17b 85 < –17(–6) ? ? 85 < 102 –6 is less than –5. Substitute –6 for b.
Holt CA Course Solving Inequalities by Multiplying or Dividing It cost Josh $85 to make candles for the craft fair. How many candles must he sell at $4.00 each to make a profit? Additional Example 3: Application Since profit is the amount earned minus the amount spent, Josh needs to earn more than $85. Let c represent the number of candles that must be sold. 4c > 85 4 c > Josh cannot sell 0.25 candle, so he needs to sell more than 21 candles to earn a profit. Write an inequality. Divide both sides by 4.
Holt CA Course Solving Inequalities by Multiplying or Dividing Check It Out! Example 3 It cost the class $15 to make cookies for the bake sale. How many cookies must they sell at 10¢ each to make a profit? Since profit is the amount earned minus the amount spent, the class needs to earn more than $15. Let c represent the number of cookies that must be sold. 0.10c > c > 150 The class must sell more than 150 cookies to make a profit. Write an inequality. Divide both sides by 0.10.