Solving Inequalities by Adding or Subtracting COURSE 3 LESSON 2-6 Solve p – 3 < –5. p – 3 < –5 Notice that 3 is subtracted from p. p – 3 + 3 < –5 + 3 Add 3 to each side. p < –2 Simplify. Check Step 1 See if –2 is a solution to the related equation. p – 3 = –5 Write the related equation. –2 – 3 –5 Substitute –2 for p. –5 = –5 Simplify. 2-6

Solving Inequalities by Adding or Subtracting COURSE 3 LESSON 2-6 (continued) Step 2 Check the inequality symbol. Choose any number less than –2 and substitute it into the original inequality. In this case, try –3. p – 3 < –5 –3 – 3 < –5 Substitute –3 for p. –6 < –5 Steps 1 and 2 both check, so p < –2 is the solution of p – 3 < –5. 2-6

Solving Inequalities by Adding or Subtracting COURSE 3 LESSON 2-6 After the hairdresser cut 3 in. from Rapunzel’s hair, her hair was at least 15 in. long. How long was her hair before she had it cut? Let l = the length before cut. Words length before cut – length cut is at least 15 in. Inequality l – 3 15 > – l – 3 15 Notice that 3 is subtracted from l. > – l – 3 + 3 15 + 3 Add 3 to each side. > – l 18 Simplify. > – Rapunzel’s hair was at least 18 in. long before she had it cut. 2-6

Solving Inequalities by Adding or Subtracting COURSE 3 LESSON 2-6 1. Graph x 6. 2. Write an inequality for k has a maximum of 4. 3. Solve r – 9 > 8. < – k 4 < – r >17 2-6