PowerPoint Presentation: Let's play now
PowerPoint Presentation: Find a number for the symbols Hint: Each symbol has a different value. They are all even numbers no bigger than 10. The values given are sum of the symbols in the boxes horizontally and vertically
PowerPoint Presentation: 24 14 14 16 18 18 18 18 16 24 14 14 16 18 18 18 18 16 24 14 14 24 14 14
PowerPoint Presentation: Now, can you write equations showing how you found the values
PowerPoint Presentation: Solving Linear Equations
PowerPoint Presentation: Review of linear equations. Construct and solve simple linear equations with variables on both sides. Represent problems mathematically, making correct use of symbols. LESSON OBJECTIVES
PowerPoint Presentation: Solve x + 1 = 7 1 x Picture a set of weighing scales The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced 1 1 1 1 1 1 1 This leaves us with: x = 6 EXAMPLE 1
PowerPoint Presentation: Solve 3 x + 5 = 14 1 x x x Picture a set of weighing scales The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced 1 1 1 1 1 This leaves us with: 3 x = 9 Which means that: x = 3 1 1 1 1 1 1 1 1 1 1 1 1 1 EXAMPLE 2
PowerPoint Presentation: Solve 5 x + 1 = 2 x + 7 1 x x x x x x x Picture a set of weighing scales The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced 1 1 1 1 1 1 1 To check if this is correct: put x = 2 5 x + 1 = 5 2 + 1 = 10 + 1 = 11 2 x + 7 = 2 2 + 7 = 4 + 7 = 11 This leaves us with: 3 x = 6 Which means that: x = 2 3 x + 1= 7 Now we have: EXAMPLE 3
PowerPoint Presentation: Solve 3 x + 10 = 5 x + 2 x x x Picture a set of weighing scales The scales are perfectly balanced Removing the same weights from BOTH sides will keep the scales balanced This leaves us with: 1 1 1 x x x x 1 1 1 1 1 x 1 1 1 1 8 = 2 x Which means that: 4 = x EXAMPLE 4
WORKSHEET: WORKSHEET Solve the following equations. 1) 4 x + 2 = 3 x + 12 2) 4 x 2 = 3 x + 12 3) 3 x + 1 =2 x + 9 4) 3 x 1 = 2 x + 9 5) 4 x + 4 = 2 x + 8 6) 3 x 4 = x + 8 7) 5 x + 5 = 2 x + 20 8) 3 x 15 = 2 x + 7 9) 4 x + 6 = 2 x - 6 10) 4 x + 10 = x + 40
SOLUTION: 4 x + 2 = 3 x + 12 subtract 3 x from both sides: x + 2 = 12 subtract 2 from both sides: x = 10 SOLUTION
SOLUTION: 4 x 2 = 3 x + 12 subtract 3 x from both sides: x 2 = 12 add 2 to both sides: x = 14 SOLUTION
SOLUTION: 3 x + 1 = 2 x + 9 subtract 2 x from both sides: x + 1 = 9 subtract 1 from both sides: x = 8 SOLUTION
SOLUTION: 3 x 1 = 2 x + 9 subtract 2 x from both sides: x 1 = 9 add 1 to both sides: x = 10 SOLUTION
SOLUTION: 4 x + 4 = 2 x + 8 subtract 2 x from both sides: 2 x + 4 = 8 subtract 4 from both sides: 2 x = 4 divide by 2: x = 2 SOLUTION
SOLUTION: 3 x 4 = x + 8 subtract x from both sides: 2 x 4 = 8 add 4 to both sides: 2 x = 12 divide by 2: x = 6 SOLUTION
SOLUTION: 5 x + 5 = 2 x + 20 subtract 2 x from both sides: 3 x + 5 = 20 subtract 5 from both sides: 3x = 15 divide by 3: x = 5 SOLUTION
SOLUTION: 3 x 1 5 = 2 x + 7 subtract 2x from both sides : x 15 = 7 Add 15 to both sides: x = 22 SOLUTION
SOLUTION: 4 x + 6 = 2 x - 6 subtract 2 x from both sides: 2 x + 6 = - 6 subtract 6 to both sides: 2 x = - 12 divide by 2: x = - 6 SOLUTION
SOLUTION: 4 x + 10 = x + 40 subtract x from both sides: 3 x + 10 = 40 subtract 10 from both sides: 3 x = 30 divide by 3: x = 10 SOLUTION
PowerPoint Presentation: _ ___ ______ __ _ ___________ ________ _______ __ _____ _____ ___ _____ ___ ___ _________ __ __ ___ __ ___ ______ ___ ____ ___ ____
PowerPoint Presentation: x 3x x 3x Lets say the width = x cm So the length = 3x cm
PowerPoint Presentation: Area = length x Width Perimeter = x +3 x + x +3 x That means : 8 x = 24 = 24 So : x = 3 Hence: width = 3cm And Length = 3 x 3 = 9cm Area = 27cm 2 = 9 x 3 = 27 x 3x x 3x
PowerPoint Presentation: __ ____ __ ____ _ _________ ______
PowerPoint Presentation: You should now be able to form and identify simple linear equations You should be able to solve linear equations with variables on both sides Represent problems mathematically, making correct use of symbols SUMMARY