2Simple 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.
3Complex 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.
6Fractional 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
7This 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
8Example 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.
9Exercise: Solve the following fractional equations