Inequalities in Mathematics
Inequalities in mathematics involve comparing numbers using symbols to show relationships such as greater than, less than, or equal to. This content covers identifying the largest numbers in pairs, defining equal values, exploring inequalities, and solving equations with gaps. Dive into the world of mathematical comparisons!
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Presentation Transcript
Starter Choose the biggest number in each pair of numbers below. 7 and 1 6 and 2 -2 and -1 -1 and 1 5 and -6 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 6 5 + 6 = ___ + 8 ___ + 3 = 10 + 2 ___ + 11 = 16 + 9 12 7 + ___ = 8 + 5 5 + 7 = ___ + 6 32 + 13 = 26 + ___ 9 6 19
What is an inequality? 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 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 a) x > 2 b) x > 11 c) x > -3 d) x 12 e) x 18 f) x 3
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
Reminder on solving inequalities 5x 2 < 28 + 2 + 2 5x < 30 5 x < 6 4x 3 2x + 7 - 2x - 2x 2x 3 7 + 3 2x 10 2 x 5 5 + 3 2
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. 2s + 4t 15
Joes cell phone costs him $21 per month plus $3 for every 1GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of $30? 21 + 3d 30 - 21 3d 7 3 d 2.333 - 21 3 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? 5h - 8 < h + 8 - h - h 4h - 8 < 8 + 8 4h < 16 4 h < 4 Hamish started with less than 4. + 8 4
Answers 6. 1. 4f + 10e 20 10 visits 2. 7 books 7. Sam = 2, Alex = 5 Sam = 1, Alex = 4 Sam = 0, Alex = 3 3. 6 miles 4. 5 nights 8. 12 < x 13 5. 7 plants
Write five possible whole numbers which x can be for each inequality 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 a) x < 10 b) x < 93 c) x < -5 d) x 6 e) x 2 f) x 0
Which statements go with which inequality? x < y x is less than or equal to y y is less than x x > y y is greater than or equal to x x is less than y x y y is less than or equal to x x is greater than or equal to y x y y is greater than x x is greater than y
Put the correct symbols (< or >) between these pairs of numbers: 5 8 7 < > 2 -1 3 > < > 4 -6 0 4 9 -2 > > > -3 1 7 3 2 -1 < > > -4 -9 9 -2 4 -6 > > < -5 -1 2 -1 -3 1 <
Write five possible whole numbers which x can be for each inequality 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 a) 5 < x < 10 b) 11 < x < 16 c) -5 < x < 0 d) 3 x 7 e) 12 x 19 f) -2 x 3
x x is greater than or equal to x x is less than or equal to x > 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 3x + 8 = 11 2x + 9 = 19 23 = 4x 5 1 = 4x + 5 12x 25 = 5x 4 7x 42 = 2x 7 6 2x = 11 7x -3x 5 = x + 15 2(5x + 2) = 4(2x + 3) 5(2x + 3) = 3(3x + 5) 6(3x + 6) = 4(5x + 2) 3(5x 1) = 2(7x + 2)
Answers x = 1 x = 5 x = 7 x = -1 x = 3 x = 7 x = 1 x = -5 x = 4 x = 0 x = 14 x = 7
x x is greater than or equal to x x is less than or equal to x > x is greater than x < x is less than
Solving Linear Inequalities 2x + 1 7 -1 from both sides 2x 6 Divide both sides by 2 x 3
Solving Linear Inequalities 3(x 4) < 18 Expand the brackets 3x 12 < 18 +12 to both sides 3x < 30 x < 10 Divide both sides by 3
Solving Linear Inequalities 4(x 4) x - 1 Expand the brackets 4x 16 x - 1 -x from both sides 3x 16 -1 +16 to both sides 3x 15 x 5 Divide both sides by 3
Graphing Inequalities SOLID line if less/greater than or equal to 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
Graphing Inequalities DOTTED line if less/greater than but not equal to 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
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
