2 Simple Linear Equations. There are two main methods of solving linear equations:Balanced MethodRemovalist MethodsThe second method is a more formal solution to solving any equation.Example : Solve 2x + 4 = 18How many of these steps DO YOU have to show?That is the real question for you need to address.Solution2x + 4 = 182x =2x = 14x = 14 ÷ 2x = 7Here a a shorter solution:2x + 4 = 182x = 14x = 7But, this is the minimum number of steps to be shown.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 - 17Solution:5x + 9 = 3x - 17Remove the 3x from the RHS, by subtracting 3x from both sides.2x + 9 = - 17Remove the +9 from the LHS, by subtracting 9 from both sides.2x = - 22Remove the 2 from the LHS, by dividing both sides by 2.x = - 11Example 2: Solve x = 3x - 17Solution:25 - 7x = 3x - 17Remove the 3x from the RHS, by subtracting 3x from both sides.x = - 17Remove the +25 from the LHS, by subtracting 25 from both sides.-10x = - 42Remove the -10 from the LHS, by dividing both sides by -10.x = 4.2Note: There are a few different way to solve this equation.
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 12.324Cancel the denominators and multiply by the factors remaining.3(2x + 1) - 2(2x - 3) = 4(7)Expand the brackets, take care with negative term in front of the brackets.6x x + 6 = 28The original equation could have been written as:2x + 9 = 282x = 19x = 91/2
7 This type of equation can be solved faster The LCM of (x - 4) and (x + 3) is (x - 4)(x + 3).Multiply each fraction by (x - 4)(x + 3).This is the correctmathematical method but not the fastest method.Exampleb)Cancel common factors.3(x + 3) = 5(x - 4)Expand brackets and solve.3x + 9 = 5x - 20This type of equation can be solved fasterBy cross-multiplying the denominators.-2x + 9 = - 20-2x = - 29x = 141/2
8 Example c) Common Error In this case , cross-multiply the denominators (for speed).Expand the brackets.Cancel common factors, must be linear equations!Solve, taking care!Common ErrorIn the following equation, the whole number must be written as a fraction with a denominator of 1.
9 Exercise: Solve the following fractional equations