6.3 Solving Multi-Step Inequalities Indicators: PFA7, PFA8, PFA9, NS4 Designed by Skip Tyler, Varina High School Edited by Eddie Judd, Crestwood Middle School

1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 {m l m > 4} + 8 + 8 5m > 20 5 5 {m l m > 4} 5(4) – 8 = 12 Add 8 to both sides Simplify Divide both sides by 5 Simplify in set notation Check your answer Graph the solution o 4 5 3

2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 {a l a < -2} - 12 - 12 -3a > 6 -3 -3 {a l a < -2} 12 - 3(-2) = 18 Subtract 12 from both sides Simplify Divide both sides by -3 Simplify in set notation (Switch the inequality!) Check your answer Graph the solution o -2 -1 -3

Which graph shows the solution to 2x - 10 ≥ 4? . Answer Now

3) Solve 5m - 4 < 2m + 11 o -2m -2m 3m - 4 < 11 + 4 + 4 + 4 + 4 3m < 15 3 3 {m l m < 5} 5(5) – 4 = 2(5) + 11 Subtract 2m from both sides Simplify Add 4 to both sides Divide both sides by 3 Simplify in set notation Check your answer Graph the solution o 5 6 4

4) Solve 2r - 18 ≤ 5r + 3 ● -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 - 3 - 3 -21 ≤ 3r 3 3 {r l r ≥ -7} 2(-7) – 18 = 5(-7) + 3 Subtract 2r from both sides Simplify Subtract 3 from both sides Divide both sides by 3 Simplify in set notation Check your answer Graph the solution ● -7 -6 -8

6) Solve -2x + 6 ≥ 3x - 4 {x l x ≥ -2} {x l x ≤ -2} {x l x ≥ 2} Answer Now

5) Solve 26p - 20 > 14p + 64 o -14p -14p 12p – 20 > 64 + 20 + 20 + 20 + 20 12p > 84 12 12 {p l p > 7} 26(7) – 20 = 14(7) + 64 Subtract 14p from both sides Simplify Add 20 to both sides Divide both sides by 12 Simplify in set notation Check your answer Graph the solution o 7 8 6

What are the values of x if 3(x + 4) - 5(x - 1) < 5? {x l x < -6} {x l x > -6} {x l x < 6} {x l x > 6} Answer Now

Assignment Pg 311 11-33 odds and 34-38 all Pg 305 13-33 odds and 43-49 odds.