1. Solve: (3x + 4√5) = 2 (3x - 4√3)

3. Lesson Objective Understand about errors in rounding Be able to solve linear inequalities Focus in particular with issues surrounding multiplying by a variable

4. More importantly we see inequality signs a lot when describing situations and we need to be able to deal with the algebra associated with them

6. x < 6 3 > x x ≥ 14 x < -4 x 0.5 x>-0.5 or x <-1

8. Important points when manipulating inequalities: 1)Never multiply both sides by a variable that might be negative!

9. Important points when manipulating inequalities: 1)Never multiply both sides by a variable that might be negative! 2) NEVER multiply both sides by a variable that might be negative!

10. Important points when manipulating inequalities: 1)Never multiply both sides by a variable that might be negative! 2) NEVER multiply both sides by a variable that might be negative!

11. Important points when manipulating inequalities: 1)Never multiply both sides by a variable that might be negative! 2) NEVER multiply both sides by a variable that might be negative! 3) NEVER MULTIPLY BOTH SIDES BY A VARIABLE THAT MIGHT BE NEGATIVE !

12. Important points when manipulating inequalities: 1)Never multiply both sides by a variable that might be negative! 2) NEVER multiply both sides by a variable that might be negative! 3) NEVER MULTIPLY BOTH SIDES BY A VARIABLE THAT MIGHT BE NEGATIVE! This does beg the question, how then do we deal with things like: where the variable is ‘underneath’?

13. So what should you do? Method 1: Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide what range of values satisfy the inequality.

14. So what should you do? Method 1: Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide what range of values satisfy the inequality.

17. So what should you do? Method 1: Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied. OR Method 2: Multiply both sides by the square of the variable because we know that the square will be positive, no matter if the original was negative Fine for single maths

18. So what should you do? Method 1: Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied. OR Method 2: Multiply both sides by the square of the variable because we know that the square will be positive, no matter if the original was negative OR Method 3: Collect everything as a single term on one side of the inequality by adding, subtracting and factorising. Then use a table to determine when the inequality is satisfied. Advanced Technique Fine for single maths

19. Lesson Objective Be able to solve quadratic inequalities Eg 1 Solve 2x 2 < 5x + 12 Hence solve a) 2x 2 – 5x – 12 ≤ 0 b) 2x 2 – 5x – 12 > 0

20. Lesson Objective Be able to solve quadratic inequalities Eg 1 Solve 2x 2 < 5x + 12 Hence solve a) 2x 2 ≤ 5x + 12 b) 2x 2 > 5x + 12 Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied.

22. Solve these inequalities: 1)x 2 < 25 2)x 2 ≥ 7 3)2x 2 < 9x + 5 4)6x 2 – x – 1 > 0