Linear Inequalities KUS objectives BAT solve all linear

Linear Inequalities KUS objectives BAT solve all linear Inequalities Starter: identify each inequality 3 4 5 6 7 8 9

Example 1 WB 16 a Starter: inequalities notation 3 • Solve this just as you would solve a normal equation 345 6789

Example 2 WB 16 b • Starter: inequalities notation 3 345 6789

Example 3 WB 16 c Brackets Starter: inequalities notation 3 • 456 789

Example 4 WB 16 d Brackets by expanding Starter: inequalities notation 3 345 6789

WB 16 e x both sides inequalities notation 3 8 10 12 14

WB 1 f x both sides inequalities notation 3 8 10 12 14

Example 6 i WB 16 g negative coefficients of x Starter: inequalities notation 3

Example 6 ii WB 16 h negative coefficient of x – alternative method Starter: inequalities notation 3 oops Inequalities: If you change the signs the symbol changes!

Problems in context WB 17 question in context The car park of a rectangular supermarket has a Perimeter fence at least 400 m long. The length of the car park is 12 m longer than the width. (i) Form an Inequality and solve it The fence used for the car park comes in sections that cost £ 28 per section. The supermarket manager has worked out they can buy the fencing for less than £ 560 (ii) Form an Inequality and solve it

WB 18 Sketch these graphs showing where they cross the axes and any turning points Check your answers on graph software

WB 19: Quadratic Inequalities

Starter: x squared greater than 16 WB 19: Quadratic Inequalities If Starter: inequalities notation 3 • Then 16 -4 4

Starter: x squared less than 9 WB 19: Quadratic Inequalities If • Starter: inequalities notation 3 9 -3 3

WB 19: Quadratic Inequalities • Starter: inequalities notation 3 81 -12 -3 6

WB 19: Quadratic Inequalities on number lines / the x-axis alone -4 -2 0 2 4 6 8 -3 -2 -1 0 1 2 3 -12 -9 -6 -3 0 3 6 9

Quadratic inequalities are easier to solve if we make one side zero WB 20 a Answers above zero Then roots -9 2 x values that work

Quadratic inequalities are easier to solve if we make one side zero WB 20 b Then roots 2 6 Answers below or equal to zero

WB 21 what to do if coefficient of x squared is negative part I Answers greater than zero Then roots 5 -2 x values that work

WB 21 what to do if coefficient of x squared is negative part II Then roots -2 5 Answers less than zero

WB 22 Practice Solve these Inequalities. Starter: inequalities notation 3 Draw a graph to help you each time

KUS objectives BAT solve linear and quadratic Inequalities self-assess One thing learned is – One thing to improve is –

END