20/11/2018 INEQUALITY NOTATION

20/11/2018 Symbols …is EQUAL to …is APPROXIMATELY equal to …is NOT equal to …is LESS THAN …is GREATER THAN …is less than OR EQUAL TO …is greater than OR EQUAL TO

20/11/2018 Task – read the following inequalities and write what they mean in words 1. x > 9 x is greater than 9 2. x > -1 x is greater than -1 3. p  6 p is greater than or equal to 6 4. a  - 4 a is greater than or equal to - 4 5. 0 < n < 3 n is greater than 0 but less than 3 6. -5  n < 2 n is greater than or equal to -5 but less than 2 7. -7  n  -1 n is greater than or equal to -7 but less than or equal to -1

20/11/2018 Number line notation A HOLLOW circle means that the number itself is NOT included So means < or > A SOLID circle means that the number itself IS included So means ≤ or ≥

20/11/2018 Examples x < 9 ‘x is less than 9 x > 5 ‘x is greater than 5’ 5 x ≤ 6 ‘x is less than or equal to 5’ 6 3 ≤ x < 10 ‘x is greater than or equal to 3 but less than 10’ 3 10

20/11/2018 x  -2 x > 4 x  -2 x < 4 -5  n  5 -1 < n  4 Task – Write down the inequality represented by each number line x  -2 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 x > 4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 x  -2 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 x < 4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -5  n  5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -1 < n  4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -5 < n < 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -3  n < 6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

20/11/2018 Task – draw a number line to represent each of these inequalities 0  n  5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -5 < n  4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 0 < n < 5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -5  n < -3 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

FINDING INTEGER SOLUTIONS 20/11/2018 FINDING INTEGER SOLUTIONS

List the integer values that satisfy this inequality. 20/11/2018 Integer values that satisfy an inequality Integer means WHOLE NUMBER Just write down all the whole numbers that make the inequality true Example –3 < x ≤ 5 List the integer values that satisfy this inequality. The integer values that satisfy this inequality are –2, –1, 0, 1, 2, 3, 4, 5.

20/11/2018 Discussion – how many inequalities can you find which describe this list of integers –4, –3, –2, –1, 0, 1 There are four possible inequalities that give this solution set, –5 < x < 2 –4 ≤ x < 2 –5 < x ≤ 1 –4 ≤ x ≤ 1

20/11/2018 Exam questions

On your mini whiteboards… Quick Questions! 20/11/2018 INTEGER SOLUTIONS On your mini whiteboards… Quick Questions!

20/11/2018 n ≤ 6 . . .1,2,3,4,5 7,8,9,10 … 6,5,4,3… 6 ,7 ,8,9…

20/11/2018 p ≥ 8 9,10,11,… ….2,3,4,5,6,7 …5,6,7,8 8, 9,10,11…

20/11/2018 n < 4 4,5,6,7… 3,4,5,6… 3,2,1….. 4,3,2,1….

20/11/2018 w > -1 0,1,2,3,4… -1, 0, 1, 2… -1,-2,-3,-4 … -2,-3,-4,…

20/11/2018 p ≤ -5 -4,-3,-2…. -5 -6,-7,-8… 5,6,7,8.. -5,-4,-3…

20/11/2018 2 ≤ n < 6 1,2,3,4,5,6 2,3,4,5,6 2,3,4,5 3,4,5,6

20/11/2018 -3 ≤ n < 5 -2,-1,0 ... 3,4,5 -4,-3,-2…3,4,5 -3 -2,-1 …4,5 -3,-2,-1 … 3,4

20/11/2018 n ≤ 6 5,4,3,2,1… 6,7,8,9,…. 6,5,4,3 …. 7, 8,9,10 …

20/11/2018 n +1 < 6 5,4,3,2…. 6,7,8,9 …. 4,3,2,1…. 5,6,7,8 …

20/11/2018 5p ≥ 30 5,6,7,8 …. 6,5,4,3,2,1 …. 7,8,9,10 …. 6,7,8,9 ….

20/11/2018 n – 3 > 7 10,11,12,13…. 10,9,8,7,6….. 11,12,13,14…. 9,8,7,6,5 ….

20/11/2018 SOLVING INEQUALITIES

20/11/2018 Solving inequalities Solve exactly as if it were an equation The only difference is if you want to × or ÷ by a NEGATIVE You must FLIP THE INEQUALITY

20/11/2018 Example Solve 2𝑥 − 1 ≤ 4

20/11/2018 Example Solve 2𝑥 + 3 ≤ 5𝑥 + 7

20/11/2018 Example Solve 10 – 3𝑥 < 30 + 2𝑥

Mini whiteboards… Quick Questions! 20/11/2018 SOLVING INEQUALITIES Mini whiteboards… Quick Questions!

20/11/2018 Solve 3t - 4 > 11 t > 5

20/11/2018 Solve 3y - 12 ≤ y - 4 y ≤ 4

20/11/2018 Solve 7 < 2x + 1 < 13 3 < x < 6

20/11/2018 Solve 11 ≤ 3x + 5 < 17 2 ≤ x < 4

20/11/2018 Solve 7 - 2x > 5x - 7 x < 2

20/11/2018 Solve -3x < -x + 8 x > -4

Solve the inequality 3𝑥 – 5 > 13 20/11/2018 Solve the inequality 3𝑥 – 5 > 13 𝑥 > 6 Solve the inequality 2𝑥 – 3 < 6 𝑥 < 4.5

Solve the inequality 5𝑥 – 3 > 3𝑥 + 5 20/11/2018 Solve the inequality 5𝑥 – 3 > 3𝑥 + 5 𝑥 > 4 Solve the inequality 𝑥 – 7 < 4𝑥 + 2 𝑥 <−3

20/11/2018 Harder types

20/11/2018 Example Solve 12<10+ 3𝑥<52

Solve the inequality 5 < 2𝑥 – 1 < 13 20/11/2018 Solve the inequality 5 < 2𝑥 – 1 < 13 3 < 𝑥 < 7 Solve the inequality 2 < 12 – 5𝑥 < 27 2 > 𝑥 > −3 OR −3 < 𝑥 < 2