The document provides instructions and examples for solving simple and double linear inequalities. It includes solving individual inequalities by performing inverse operations and combining separate inequalities connected by "and" or joined by commas into a double inequality involving "less than" or "greater than". Students are given examples to practice solving inequalities involving addition, subtraction, multiplication and division.

2. SOLVE THESE INEQUALITIES 1) x + 10 ≤ 38 x + 10 – 10 ≤ 38 - 10 x ≤ 28 2) x – 15 > 25 x – 15 + 15 > 25 + 15 x > 40 23 24 25 26 27 28 29 39 40 41 42 43 44 45

3. Try these… Solve and write down the first five possible value for x if x is a whole number and: x + 8 > -5 Solve and write down one possible value for x if x is a prime number. x – 8 ≤ 4

4. Solve These Inequalities. 3) 4x < 28 4x 4 < 28 4 x < 7 4) 2x + 5 ≥ 13 2x + 5 – 5 ≥ 13 - 5 2x ≥ 8 2x 2 ≥ 8 2 x ≥ 4

5. Try these… 1) 4x – 3 ≤ -7 4) -12 < 3(2y – 4) http://www.math-play.com/Inequality-Game.html a 3 + 9 > 12 2) 3) 4 ≤ 5x – 2 7

7. DOUBLE INEQUALITY 5) Solve 15 < 4x + 7 < 19 Solve each inequality in turn. 15 < 4x + 7 15 – 7 < 4x 8 < 4x 8 4 < 4x 4 2 < x 4x + 7 < 19 4x < 19 - 7 4x < 12 x < 3 Put them together 2 < x < 3

8. DOUBLE INEQUALITY Try this … 6) Solve 23 < 4x + 3 < 39 23 < 4x + 3 23 – 3 < 4x 20 < 4x 5 < x 4x + 3 < 39 4x < 39 - 3 4x < 36 x < 9 5 < x < 9 Pg 331 Ex 15:10 # 7 – 12 Ex 15:11 ALL

9. FASTER BUT HARDER METHOD 14 ≤ 3x + 5 ≤ 26 ≤ 3x + 5 – 5 ≤ 26 - 5 14 – 5 9 ≤ 3x ≤ 21 9 3 ≤ ≤ 3x 3 21 3 3 ≤ ≤ x 7

10. TRY THIS… Solve for x: -5 < 4x + 3 ≤ 23 Pg 332 Ex 15:12 Odd