Starter Choose the biggest number in each pair

Starter Choose the biggest number in each pair of numbers below. 7 and 1 -1 and 1 6 and 2 5 and -6 -2 and -1 0 and -4

What does equal mean? Exactly the same value! Complete the equations below by filling in the gaps – make sure both sides are equal. 3 +8 5 + 6 = ___ 6 =8+5 7 + ___ 9 + 3 = 10 + 2 ___ 6 +6 5 + 7 = ___ 12 + 11 = 16 + 9 ___ 19 32 + 13 = 26 + ___

What is an inequality? Inequality Not equal to Greater than Less than

Inequality Symbols > greater than ≥ greater than or equal to For example, 6 is greater than 3 6>3

Write five possible whole numbers which x can be for each inequality a) b) c) d) e) f) x>2 x > 11 x > -3 x ≥ 12 x ≥ 18 x≥ 3 3, 4, 5, 6, 7… 12, 13, 14, 15, 16… -2, -1, 0, 1, 2… 12, 13, 14, 15, 16… 18, 19, 20, 21, 22… 3, 4, 5, 6, 7…

Inequality Symbols < less than ≤ less than or equal to For example, 4 is less than 9 4<9

Starter – Inequalities Bingo Draw a 3 x 3 grid and fill it with 9 of the inequalities from below. x < -1 x<0 x<1 x<2 x > -1 x>0 x>1 x>2 x ≤ -1 x≤ 0 x≤ 1 x≤ 2 x ≥ -1 x≥ 0 x≥ 1 x≥ 2

-4 -3 -2 -1 0 1 2 3 4

Reminder on solving inequalities… 5 x – 2 < 28 +2 +2 5 x < 30 ÷ 5 x <6 4 x – 3 ≥ 2 x + 7 - 2 x 2 x – 3 ≥ +3 2 x +3 ≥ ÷ 2 x 7 10 ÷ 2 ≥ 5

Mrs. Bradshaw is making treats for a tea party later this week, and she has up to 15 eggs to use for this purpose. A batch of scones requires 2 eggs and a batch of miniature tarts requires 4 eggs. Write an inequality that describes this situation. 2 s + 4 t ≤ 15

Joe’s cell phone costs him $21 per month plus $3 for every 1 GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of $30? 21 + 3 d ≤ 30 - 21 3 d ≤ 7 ÷ 3 d ≤ 2. 333… Joe can download 2 GB of data without going over his monthly budget.

Gloria starts with five times as much money as Hamish. Gloria gives £ 8 to Hamish, and then Hamish has more money than Gloria. How much money did Hamish start with? 5 h - 8 < h + 8 -h -h 4 h - 8 < +8 4 h ÷ 4 h 8 +8 < 16 ÷ 4 < Hamish started with less than £ 4. 4

Answers 1. 4 f + 10 e ≥ 20 6. 10 visits 2. 7 books 7. 3. 6 miles Sam = 2, Alex = 5 Sam = 1, Alex = 4 Sam = 0, Alex = 3 4. 5 nights 8. 12 < x ≤ 13 5. 7 plants

Write five possible whole numbers which x can be for each inequality a) b) c) d) e) f) x < 10 x < 93 x < -5 x≤ 6 x≤ 2 x≤ 0 9, 8, 7, 6, 5… 92, 91, 90, 89, 88… -6, -7, -8, -9, -10… 6, 5, 4, 3, 2… 2, 1, 0, -1, -2… 0, -1, -2, -3, -4…

Which statements go with which inequality? y is less than x x<y x is less than or equal to y y is greater than or equal to x x>y x is less than y y is less than or equal to x x≤y x is greater than or equal to y y is greater than x x≥y x is greater than y

Put the correct symbols (< or >) between these pairs of numbers: 5 < 8 7 > 3 2 > -1 0 < 4 9 > -2 4 > -6 7 > 3 2 > -1 -3 < 1 9 > -2 4 > -6 -4 > -9 2 > -1 -3 < 1 -5 < -1

Write five possible whole numbers which x can be for each inequality a) b) c) d) e) f) 5 < x < 10 11 < x < 16 -5 < x < 0 3≤x≤ 7 12 ≤ x ≤ 19 -2 ≤ x ≤ 3 6, 7, 8, 9 12, 13, 14, 15 -4, -3, -2, -1 3, 4, 5, 6, 7 12, 13, 14, 15, 16, 17, 18, 19 -2, -1, 0, 1, 2, 3

x ≥ x is greater than or equal to x ≤ x > x is less than or equal to x is greater than x < x is less than

x≥ 3 x < 10

x≤ 5 2<x≤ 8

Pair Activity Complete the Tarsia jigsaw, matching the inequalities to those displayed on the number lines.

Starter 3 x + 8 = 11 23 = 4 x – 5 2 x + 9 = 19 1 = 4 x + 5 12 x – 25 = 5 x – 4 6 – 2 x = 11 – 7 x 7 x – 42 = 2 x – 7 -3 x – 5 = x + 15 2(5 x + 2) = 4(2 x + 3) 6(3 x + 6) = 4(5 x + 2) 5(2 x + 3) = 3(3 x + 5) 3(5 x – 1) = 2(7 x + 2)

Answers x=1 x=7 x=5 x = -1 x=3 x=1 x=7 x = -5 x=4 x = 14 x=0 x=7

x ≥ x is greater than or equal to x ≤ x > x is less than or equal to x is greater than x < x is less than

Solving Linear Inequalities 2 x + 1 ≥ 7 2 x ≥ 6 x≥ 3 -1 from both sides Divide both sides by 2

Solving Linear Inequalities 3(x – 4) < 18 3 x – 12 < 18 3 x < 30 x < 10 Expand the brackets +12 to both sides Divide both sides by 3

Solving Linear Inequalities 4(x – 4) ≤ x - 1 4 x – 16 ≤ x - 1 3 x – 16 ≤ -1 3 x ≤ 15 x≤ 5 Expand the brackets -x from both sides +16 to both sides Divide both sides by 3

Answers

Graphing Inequalities On a set of axes, show the set of values that satisfy the inequality; x≤ 2 Draw the line showing; x=2 But the inequality is saying a range of values… SOLID line if less/greater than or equal to

Graphing Inequalities On a set of axes, show the set of values that satisfy the inequality; y < -5 Draw the line showing; y = -5 But the inequality is saying a range of values… DOTTED line if less/greater than but not equal to

Graphing Inequalities On a set of axes, show the set of values that satisfy the inequality; y>x Draw the line showing; y=x But the inequality is saying a range of values…

A x<5 B x≤ 5 C y<5 D y≤ 5

A x>5 B x≥ 5 C y>5 D y≥ 5

A B C D