Solving Two-Step Inequalities Designed by Skip Tyler, Varina High School

Solving an inequality is similar to solving an equation, with one main difference. If you divide the inequality by a negative number, you switch the direction of the symbol.

1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 5(4) – 8 = 12 + 8 + 8 5m > 20 5 5 m > 4 5(4) – 8 = 12 Draw “the river” Add 8 to both sides Simplify Divide both sides by 5 Check your answer Graph the solution o 4 5 3

2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 Draw “the river” Subtract 12 from both sides Simplify Divide both sides by -3 Simplify (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 < 5 5(5) – 4 = 2(5) + 11 Draw “the river” Subtract 2m from both sides Simplify Add 4 to both sides Divide both sides by 3 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 -7 ≤ r or r ≥ -7 2(-7) – 18 = 5(-7) + 3 Draw “the river” Subtract 2r from both sides Simplify Subtract 3 from both sides Divide both sides by 3 Check your answer Graph the solution ● -7 -6 -8

6) Solve -2x + 6 ≥ 3x - 4 x ≥ -2 x ≤ -2 x ≥ 2 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 > 7 26(7) – 20 = 14(7) + 64 Draw “the river” Subtract 14p from both sides Simplify Add 20 to both sides Divide both sides by 12 Check your answer Graph the solution o 7 8 6

What are the values of x if 3(x + 4) - 5(x - 1) < 5? Answer Now