Math 017 Materials With Exercises

sides (subtracting 4 x from both sides would also becorrect).4x x 5 15Collect like terms.3x 5 15Add 5 to both sides3x 15 5 Perform the operation of addition.3x 20 Divide both sides by 3.20x 320The solution of 4 x 5 15 x is x .3Checking solution of a linear equationsIt is always possible to check your solution. To this end, replace the variable in the original equationwith the value of the solution and verify that the left-hand side of the equation is equal to the righthandside. For example, to check that x 5 is indeed a solution of the equation3(x 2) 9, substitute5 for x in the equation.3(5 2) 933 99 9Since the left hand side is equal to the right hand side of the equation, 5 is indeed a solution.Example 8.4 Solve the equation 3 2x 5 and check your solution.Solution:3 2x 5 Add 5 to both sides ( x was multiplied by 2 , and then 5 wassubtracted, so to „undo‟ that, we first add 5)8 2x Divide each side by 2 (divide, since x is multiplied by 2 :there is no subtraction!). Simplify. 4 xThe solution of 3 2x 5 is x 4.To check the answer we replace x with 4 in the original equation 3 2(4) 5,evaluate both sides, 3 3, and conclude that, indeed, 4 is a solution.Linear equations with no solution or a solution set consisting of all real numbersAll of the above equations had exactly one solution. However, there are some linear equations thathave no solutions. The solution set of other equations may consist of all real numbers. We will seebelow an example of an equation that has no solution, followed by an example whose solution consistsof all real numbers.82