Inequalities

Inequalities An Equation is a mathematical relationship which is balanced - what is on the left is always equal to what is on the right In an Inequality, one side is larger than the other Women’s average height is less than men’s average height

Inequlities To win a game of dice, a player must throw at least a score of 4 - i.e. equal to or greater than 4 Score ³ 4 There should be no more than 6 people standing on the bus - less than or equal to 6 Number of people standing £ 6

Inequality Signs < means “is less than”  means “is less than or equal to” > means “is greater than”  means ”is greater than or equal to” Reading Inequalities 6 < 8 or equivalently 8 > 6 1. 3 < n < 9 n is greater than 3 but less than 9. n is greater than or equal to 4 but less than 7. 2. 4  n < 7 n is greater than or equal to -2 but less than or equal to 1. 3. -2  n  1

Read the following inequalities n is greater than 0 but less than 3. 2. -5  n < 2 n is greater than or equal to -5 but less than 2. 3. -7  n  -1 n is greater than or equal to -7 but less than or equal to -1. 4. x > 9 x is greater than 9 x is greater than -1 5. x > -1 p is greater than or equal to 6 6. p  6 7. a  - 4 a is greater than or equal to - 4

Displaying Inequalities on a Number Line x  1 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 x > 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

Displaying Inequalities on a Number Line x  1 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 x < 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

Displaying Inequalities on a Number Line 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

State the inequalities displayed on each number line below. 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -5 < n  4 0 < n < 5 -5  n < -3

Understanding Inequalities In inequalities, the greater than sign (>) and the less than sign (<) relate two expressions. Divide both sides by -5 -2 < - 3 FALSE If both sides of an inequality are multiplied or divided by a negative number, the inequality sign is reversed to keep the inequality true.

x + 5x > 2 - 8 6x > -6 x > -1 Graphing Linear Inequalities on a Number Line Solve and graph: x + 8 > 2 - 5x x + 5x > 2 - 8 6x > -6 x > -1 The solid dot at -1 indicates that -1 is part of the solution: x > 1 means x > 1 and x = 1

Solve and graph: 2(x + 3) - 5x < x - 10 2x + 6 - 5x < x - 10 Graphing Linear Inequalities on a Number Line Solve and graph: 2(x + 3) - 5x < x - 10 2x + 6 - 5x < x - 10 -3x + 6 < x - 10 -3x - x < -10 - 6 -4x < -16 x > 4 Note the sign is reversed because both sides of the inequality are divided by a negative number. The open dot at 4 indicates that 4 is not part of the solution. 2.1.4

The rule for inequalities is any time you multiply (or divide) both sides by a negative number, you need to reverse the signs.

Solve each inequality:

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