Solving equations using the balancing method
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This document provides instructions on how to solve equations using a balancing method. It explains that an equation can be represented using paper or real scales by placing values on each side. To solve the equation, the same operation (such as adding, subtracting, multiplying or dividing) must be applied to both sides so that the scales remain balanced until the variable is isolated on one side. Several examples of equations and their step-by-step solutions are provided. Interactive online activities for practicing this method are also listed.
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To get/buy a soft copy, please send a request to queenyedda@gmail.com
Inclusions of the file attachment:
* Fonts used
* Soft copy of the WHOLE ppt slides with effects
* Complete activities
PRICE: P200 only
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This document provides information about different methods for solving quadratic equations. It discusses factoring the equation, using the quadratic formula, and completing the square. Step-by-step explanations are provided for each method. Factoring involves finding two binomials that multiply to give the quadratic term and add to the linear term. The quadratic formula is given as x = (-b ±√(b2 - 4ac))/2a. Completing the square requires grouping like terms and completing the square of the quadratic term.
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Algebra involves manipulating mathematical symbols according to specific rules. Linear equations contain an unknown variable represented by a letter like x. To solve linear equations, operations are performed on both sides of the equation so that the variable is isolated on one side in terms of numbers. For example, to solve x + 1 = 4, subtract 1 from both sides, resulting in x = 3. Solving techniques like adding, subtracting, multiplying, and dividing both sides are demonstrated through examples.
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Solving equations using the balancing method
- 1. Starter! A brick and a half weighs a kilo and half a brick. How much does a brick weigh?
- 2. Could we … write this real life problem as an equation? b + ½b = 1 + ½b
- 3. Learning Objectives: To solve equations with the unknown on both sides of an equation Learning Outcome: You can use the ‘balancing method’ to solve equations
- 4. What you will need to represent the equations: Paper (or real) scales x’s 1’s
- 5. Solving Equations Use your ‘scales’ to show this equation… 2x + 4 = x + 6 Solving the equation … What’s the value of x ? Remember to do the same to both sides of the equation … Remove ‘4’ from each side 2x = x + 2 Divide each side by ‘2’ x = 2
- 6. Remember! Always do the same to each side of the equation! Keep your scales balanced! E.g. 2x + 4 = x + 10 (- 4) 2x = x + 6 (- 4) (÷2) x = 6 (÷2) Remember! In an equation, each letter stands for a missing number. To solve an equation, find the values of the missing numbers. Remember! Adding and subtracting are the inverse (opposite) of each other. Multiplying and dividing are the inverse of each other.
- 7. 1. Use your scales to represent an equation 2. Solve the equation (to find the value of x) 3. Write your method down 2x + 4 = x + 6 3x + 1 = 2x + 4 4x + 2 = 2x + 4 2x + 5 = x + 9 5x + 3 = 3x + 7 3x + 4 = 2x + 10 Remember! Always do the same to each side of the equation! Keep your scales balanced!
- 8. Online Interactive Activities Balancing Method Activity: Available at http://www.mathsisfun.com/algebra/add-subtract-balance.html Algebra Equations with a Balance Scale: Available at http://www.mathplayground.com/AlgebraEquations.html Go to the website, click ‘create problem’ and type in the equation. Use the scales to represent the equation and solve!