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Revision Equations I By I Porter Linear Equations.

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Presentation on theme: "Revision Equations I By I Porter Linear Equations."— Presentation transcript:

1 Revision Equations I By I Porter Linear Equations

2 There are two main methods of solving linear equations: Balanced Method Removalist Methods The second method is a more formal solution to solving any equation. Example : Solve 2x + 4 = 18 Solution2x + 4= 18 2x= x= 14 x= 14 ÷ 2 x= 7 How many of these steps DO YOU have to show? That is the real question for you need to address. Here a a shorter solution: 2x + 4= 18 2x= 14 x= 7 But, this is the minimum number of steps to be shown. Simple Linear Equations. This is the basic method the author will use for all the PowerPoints on equations.

3 Complex Linear Equations. Solving linear equations with algebra on both sides of the equals sign. Example 1: Solve 5x + 9 = 3x - 17 Solution:5x + 9 =3x x + 9 = x = - 22 x = - 11 Remove the 3x from the RHS, by subtracting 3x from both sides. Remove the +9 from the LHS, by subtracting 9 from both sides. Remove the 2 from the LHS, by dividing both sides by 2. Example 2: Solve x = 3x x =3x x = x = - 42 x = 4.2 Remove the 3x from the RHS, by subtracting 3x from both sides. Remove the +25 from the LHS, by subtracting 25 from both sides. Remove the -10 from the LHS, by dividing both sides by -10. Solution: Note: There are a few different way to solve this equation.

4 Equations with Brackets Solving linear equations with brackets. Example 1: Solve 3(2x - 1) = 4x + 17 Solution3(2x - 1) = 4x x - 3 = 4x x - 3 = 17 2x = 20 x = 10 Example 2: Solve 4(5 - 3x) = 8x - 47 Solution4(5 - 3x) = 8x x = 8x x = x = -67 x = 3.35 or

5 Exercise: Solve the following (write answer in fraction form) a) 5x - 17 = 3x + 35b) 3(x - 9) = 4x - 25c) 4(2x - 9) = 18 - (x - 3) 5x - 17= 3x x - 17= 35 2x= 52 x= 26 3(x - 9)= 4x x - 27= 4x x= 2 x= -2 4(2x - 9)= 18 - (x - 3) 8x - 36= 18 - x + 3 9x - 36= x= 57 x= 6 1 / 3

6 Fractional Linear Equations. To solve fractional linear equations, you need to find the L.C.M. of the denominators. Examples: Solve each of the following. a) The LCM of 3, 4 and 6 is 12. Multiply each fraction by (2x + 1) - 2(2x - 3) = 4(7) 6x x + 6 = 28 2x + 9 = 28 2x = 19 x = 9 1 / 2 Cancel the denominators and multiply by the factors remaining. Expand the brackets, take care with negative term in front of the brackets. The original equation could have been written as:

7 b) The LCM of (x - 4) and (x + 3) is (x - 4)(x + 3). Multiply each fraction by (x - 4)(x + 3).This is the correct mathematical method but not the fastest method. Expand brackets and solve. 3(x + 3) = 5(x - 4) 3x + 9 = 5x x + 9 = x = - 29 x = 14 1 / 2 This type of equation can be solved faster By cross-multiplying the denominators. Example Cancel common factors.

8 c) In this case, cross-multiply the denominators (for speed). Cancel common factors, must be linear equations! Solve, taking care! Example Common Error In the following equation, the whole number must be written as a fraction with a denominator of 1. Expand the brackets.

9 Exercise: Solve the following fractional equations


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