Solve for X
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The document discusses how to solve equations by using inverse operations. It begins by defining the parts of an equation, such as coefficients, constants, and variables. Then it provides examples of solving simple one-step equations by adding or subtracting the same quantity to both sides of the equation. The document also demonstrates how to solve multi-step equations by combining like terms and isolating the variable. It emphasizes checking solutions by substituting them back into the original equation. Overall, the document provides a thorough overview of solving different types of equations through applying inverse operations.
Solve for X
- 2. SOLVING EQUATIONS show how to solve for “X” 03 March 2014 J. MBEDU 201246302 2
- 3. Solving Equations • What will we discuss? What are the parts of an equation What does it mean to solve an equation How do we use inverse operations to solve equations How to solve simple and complex equations
- 4. What are the parts of an equation? Let’s first take a look at an equation and identify its parts 3x 12 36 x 03 March 2014 J. MBEDU 201246302 4
- 5. What are the parts of an equation? Let’s first take a look at an equation and identify its parts 3x 12 36 x Coefficient Constant Variable 03 March 2014 J. MBEDU 201246302 5
- 6. Solving 1 Step Equations How much does the suitcase weigh in terms of blocks? B=Blocks S=Suitcase Equation: 6B + S = 9B -6B 03 March 2014 -6B J. MBEDU 201246302 6
- 7. Solving 1 Step Equations How much does the suitcase weigh in terms of blocks? B=Blocks S=Suitcase Equation: 6B + S = 9B -6B -6B S = 3B 03 March 2014 J. MBEDU 201246302 7
- 8. Solving 1 Step Equations How much does the suitcase weigh in terms of blocks? B=Blocks S=Suitcase Equation: 6B + S = 9B -6B -6B S = 3B What is the weight of the suitcase if each block has a weight of 2lbs. ? S = 3 (2) = 6 lbs. 03 March 2014 J. MBEDU 201246302 8
- 9. So how do we solve equations with inverse operations? Let’s take a look at a simple equation x 13 21 03 March 2014 J. MBEDU 201246302 9
- 10. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: x 13 21 - 13 - 13 Answer: 03 March 2014 x 8 J. MBEDU 201246302 10
- 11. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: x 13 21 - 13 - 13 Answer: Now that we have solved the equation, let’s check the solution: x 8 x 13 21 8 13 21 21 21 03 March 2014 J. MBEDU 201246302 11
- 12. So how do we solve equations with inverse operations? Let’s take a look at a simple equation y 5 12 03 March 2014 J. MBEDU 201246302 12
- 13. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: y 5 12 +5 +5 Answer: 03 March 2014 y 17 J. MBEDU 201246302 13
- 14. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: y 5 12 +5 +5 Answer: Now that we have solved the equation, let’s check the solution: y 17 y 5 12 17 5 12 12 12 03 March 2014 J. MBEDU 201246302 14
- 15. So how do we solve equations with inverse operations? Let’s take a look at a simple equation 25W 75 03 March 2014 J. MBEDU 201246302 15
- 16. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1 : 25W 75 Divide by 25 25 25 03 March 2014 J. MBEDU 201246302 16
- 17. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: 25W 75 25 25 75 Step 2: W 25 Answer: W 3 03 March 2014 J. MBEDU 201246302 17
- 18. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: 25W 75 25 25 Now that we have solved the equation, let’s check the solution: 25W 75 75 Step 2: W 25 25(3) 75 Answer: W 3 03 March 2014 J. MBEDU 75 75 201246302 18
- 19. So how do we solve equations with inverse operations? Let’s take a look at a simple equation A 4 16 03 March 2014 J. MBEDU 201246302 19
- 20. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1 : (16) A 4 (16) Multiply by 16 16 03 March 2014 J. MBEDU 201246302 20
- 21. So how do we solve equations with inverse operations? Let’s take a look at a simple equation A Step 1: (16) 4 (16) 16 Step 2: A 4(16) Answer: A 64 03 March 2014 J. MBEDU 201246302 21
- 22. So how do we solve equations with inverse operations? Let’s take a look at a simple equation A Step 1: (16) 4 (16) 16 Now that we have solved the equation, let’s check the solution: Step 2: A 4(16) Answer: A 64 03 March 2014 J. MBEDU 201246302 A 4 16 64 4 16 44 22
- 23. More examples X + 11 = 9 -11 -11 = -2 X X - 37 = 52 20 + h = 41 1 17 - s = 27 20 h 41 - 20 - 20 h 21 03 March 2014 X - 37 52 37 37 X 89 17 s 27 17 17 s 10 3X = 72 13 3 X = 24 s 10 10 1 1 This is the same as -1S=10 23
- 24. 1 Step Equations Continued… 1 6X = 42 6 16 x 4 7 1X=7 x 7 7 4 7 1 1 or x = 7 x 28 3 21 s 3 21 s 1 Cross Multiply 03 March 2014 s 21 3 1 3 1 s 21 7 2 P = 3 Multiply by the reciprocal of 2/5 5 4 2 5 3 5 p 5 2 4 2 15 1p 8 24
- 25. Multi Step Equations Solve: 03 March 2014 5x 2 = x + 4 J. MBEDU 201246302 25
- 26. Multi Step Equations Solve: 03 March 2014 Notice that there are variables on both sides 5x 2 = x + 4 J. MBEDU 201246302 26
- 27. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 Get rid of the -2 on the left side 03 March 2014 J. MBEDU 201246302 27
- 28. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 5x 2 = x + 4 +2 Get rid of the -2 on the left side +2 5x = x + 6 03 March 2014 J. MBEDU 201246302 28
- 29. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 5x 2 = x + 4 +2 Get rid of the -2 on the left side +2 5x = x + 6 Simplify and Get rid of the x on the right side 03 March 2014 J. MBEDU 201246302 29
- 30. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 5x 2 = x + 4 +2 Get rid of the -2 on the left side +2 5x = x + 6 Simplify and Get rid of the x on the right side 5x = x + 6 –x –x 4x = 6 03 March 2014 J. MBEDU 201246302 30
- 31. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 5x 2 = x + 4 +2 Get rid of the -2 on the left side +2 5x = x + 6 Simplify and Get rid of the x on the right side 5x = x + 6 –x –x 4x = 6 4 4 03 March 2014 J. MBEDU 201246302 31
- 32. Multi Step Equations Solve: Notice that there are variables on both sides 5x 2 = x + 4 5x 2 = x + 4 +2 Get rid of the -2 on the left side +2 5x = x + 6 Simplify and Get rid of the x on the right side 5x = x + 6 –x –x 4x = 6 4 4 03 March 2014 3 x= 2 J. MBEDU Final Answer 201246302 32
- 33. More examples No Clarifications but following same methods as all previous above Examples 03 March 2014 J. MBEDU 201246302 33
- 34. 3(b+2) +2b = 21 3b+6 +2b = 21 03 March 2014 J. MBEDU 201246302 34
- 35. 3(b+2) +2b = 21 3b+6 +2b = 21 5b+6 = 21 03 March 2014 J. MBEDU 201246302 35
- 36. 3(b+2) +2b = 21 3b+6 +2b = 21 5b+6 = 21 5b+6-6 = 21-6 03 March 2014 J. MBEDU 201246302 36
- 37. 3(b+2) +2b = 21 3b+6 +2b = 21 5b+6 = 21 5b+6-6 = 21-6 5b = 15 03 March 2014 J. MBEDU 201246302 37
- 38. 3(b+2) +2b = 21 3b+6 +2b = 21 5b+6 = 21 5b+6-6 = 21-6 5b = 15 03 March 2014 J. MBEDU 201246302 38
- 39. 3(b+2) +2b = 21 3b+6 +2b = 21 5b+6 = 21 5b+6-6 = 21-6 5b = 15 Therefore b = 3 03 March 2014 J. MBEDU 201246302 39
- 40. The End Email: Jay.mbedu@gmail.com 03 March 2014 J. MBEDU 201246302 40
- 41. Coolers used Fonts used Yellow Green red Pink Orange White Black Light Blue Purple Algerian Arabic Typesetting Bodoni MT Black Arial (Headings) Arial Tahoma (Body) Garamond Times New Roman Cambria Math Cambria 03 March 2014 J. MBEDU 201246302 41