Inequalities Note: Pretend the inequality sign is an = sign until the very last step Natural Numbers (N) Integers (Z) Real Numbers (R)

Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

Draw x > 5 x N Draw x 2 x Z Draw x 1 x R

Solutions…. You can have a range of answers…… -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers less than 2 x< 2

Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers greater than -2 x > -2

Solutions continued…. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers less than or equal to 1

Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers greater than or equal to -3

Solving an Inequality x < 8 Solve using addition: x – 3 < 5 Add the same number to EACH side. +3 +3 x < 8

Solving Using Subtraction Subtract the same number from EACH side. -6 -6

Using Subtraction… Graph the solution. -5 -4 -3 -2 -1 0 1 2 3 4 5

Using Addition… Graph the solution. -5 -4 -3 -2 -1 0 1 2 3 4 5

Solving using Multiplication Multiply each side by the same positive number. (2)

Solving Using Division Divide each side by the same positive number. 3

Solving by dividing by a negative # -2

Solving by multiplication of a negative # Multiply by (-1). (-1)

When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol

Show x > 2 on a number line Example 1 Show x > 2 on a number line Answer: This means all numbers bigger than 2 -4 -3 -2 -1 1 2 3 4 5 Example 2 Show x ≤ 3 on a number line Answer: This means all numbers less than and including 3 Example 3 Show -2 < x ≤ 1 on a number line -4 -3 -2 -1 1 2 3 4 5 Answer: This means all numbers between -2 and 1 including 1 but not -2 Continue Teaching 2 Monday, 20 May 2019 -4 -3 -2 -1 By Cang Tu 1 2 3 4 5 1st Slide

Worksheet 1 For each question, show the inequality on the number line Grade C Qu1-2 For each question, show the inequality on the number line x > 1 x ≤ 3 x ≤ -1 1 < x ≤ 4 -2 ≤ x < 2 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 Write an the inequality for each diagram a) b) c) 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 WS 2 Monday, 20 May 2019 -4 -3 -2 -1 1 2 3 4 5 1st Slide

Grade C Qu1-7 Worksheet 2 Find the solutions of these inequalities and show it on a number line 3x + 2 > 8 5x – 3 ≤ 12 2x – 7 < 1 2x - 3 > 0 3(2x + 1) ≥ 9 3x – 1< x + 5 4(x - 1) ≥ 2x – 3 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 Monday, 20 May 2019 By Cang Tu 1st Slide

Short Method Solve the compound inequality and graph the solutions. 8 < 3x – 1 ≤ 11 1. add 1 to each part of the inequality. 8 < 3x – 1 ≤ 11 +1 +1 +1 9 < 3x ≤ 12 2. divide each part of the inequality by 3 to undo the multiplication. 3 < x ≤ 4 The solution set is {x:3 < x ≤ 4}.

Solve –3 < –1 – 2x ≤ 5. Then graph the solution. Example 5 Reversing the sign Solve –3 < –1 – 2x ≤ 5. Then graph the solution. +1 +1 +1 –2 < – 2x ≤ 6 Reverse the inequalities when you divide by a negative –2 –2 –2 1 > x ≥ –3 -4 -3 -2 -1 0 1 2

Try these Solve and graph the inequality. 1. 2. 3. -2 -1 0 1 2 3 4 5 6 -2 -1 0 1 2 3 4 5 6 2. -2 -1 0 1 2 3 4 5 6 3. -10 -9 -8 -7 -6 -5 -4 -3 -2

Match the Compound Inequality with the Correct Graph 0 < x + 2 < 5 -4 + a > 1 OR -4 + a < -3 -3 < x + 2 < 3 2 < x + 2 < 5 x + 2 < -6 OR x + 2 > -2 -8 -6 -4 -4 -2 -2 2 1 3 5 2 4

Now You Try… Solve and Graph the Compound Inequality -3 < x + 2 < 7 x – 1 < -1 OR x – 5 > -1 2 < x + 2 < 5 11 < 2x + 3 < 21 n + 2 < 3 OR n + 3 > 7 -5 5 -5 < x < 5 2 4 x < 0 OR x > 4 2 4 0 < x < 3 4 6 8 4 < x < 9 x < 1 OR x > 4 1 3 5