Math 017 Materials With Exercises

■ Solve the inequality 4x 9 1. 4x 9 1Subtract 9 from both sides. 4x 9 9 19Perform the indicated operations (on each sideseparately). 4x 8Divide both sides by 4 and reverse thedirection of the inequality sign. 4x 8Cancel fractions. 4 4x 2The solution of the inequality 4x 9 1is x 2■This means that all numbers that are less than or equal to 2 make this inequality true. That is, if in theoriginal inequality x is replaced by any number less than or equal to 2, the resulting numericalstatement will always be true. It also means that any other number, i.e. any number that is greater than2, when substituted for x , would give us a false numerical statement.Observe that there are infinitely many solutions and that is why, instead of listing them, we must usethe appropriate inequality symbol in recording the result.Example 10.5 Solve the following inequalities and graph their solution.a) x 4b) 3x 7 2Solution:a) x 4Multiply both sides by 1, remember about reversing theinequality sign.( 1)(x ) ( 1)(4)Perform the indicated operations.x 4The graph of the solution:b) 3x 7 2Add 7 to both sides.3x 7 7 2 7 Simplify.3x 5Divide each side by 3.3x5 3 3Simplify.5x 3The graph of the solution:98