82Chapter PPrerequisites: Fundamental Concepts of Algebra111.When performing the divisionI began by dividing the numerator and the denominator bythe common factor,112.I subtracted from and obtained a constant.In Exercises 113–116, determine whether each statement is true orfalse. If the statement is false, make the necessary change(s) toproduce a true statement.113.114.The expression simplifies to the consecutiveinteger that follows 115.116.In Exercises 117–119, perform the indicated operations.117.118.a1-1xb a1-1x+1b a1-1x+2b a1-1x+3b1xn-1-1xn+1-1x2n-16+1x=7x2x-1x-7+3x-1x-7-5x-2x-7=0-4.-3y-6y+2x2-25x-5=x-5x-3x-13x-5x-1x+3.7xx+3,1x+322x-5,119.120.In one short sentence, five words or less, explain whatdoes to each number Preview ExercisesExercises 121–123 will help you prepare for the material coveredin the next section.121.If is substituted for xin the equationis the resulting statement true or false?122.Multiply and simplify:123.Evaluatefor .a=2, b=9, and c= -5-b-2b2-4ac2a12ax+24-x-13b.2(x-3)-17=13-3 (x+2),6x.1x+1x2+1x31x4+1x5+1x61x-y2-1+1x-y2-2P.7EquationsObjectivesSolve linear equations inone variable.Solve linear equationscontaining fractions.Solve rational equations withvariables in the denominators.Solve a formula for a variable.Solve equations involvingabsolute value.Solve quadratic equations byfactoring.Solve quadratic equations bythe square root property.Solve quadratic equations bycompleting the square.Solve quadratic equationsusing the quadratic formula.Use the discriminant todetermine the number andtype of solutions of quadraticequations.Determine the most efficientmethod to use when solving aquadratic equation.Solve radical equations.S e c t i o nMath tattoos. Who knew?Do you recognize thesignificance of this tattoo?The algebraic expression givesthe solutions of a quadraticequation.In this section, we willreview how to solve a variety ofequations,including linearequations, quadratic equations,and radical equations.Solving Linear Equations in One VariableWe begin with a general definition of a linear equation in one variable.Definition of a Linear EquationA linear equation in one variable is an equation that can be written in the formwhere and are real numbers, and aZ0.baax+b=0,xAn example of a linear equation in one variable is4x+12=0.

Section P.7Equations83Solving an equationin involves determining all values of that result in a truestatement when substituted into the equation. Such values are solutions, or roots, ofthe equation. For example, substitute for in We obtainThis simplifies to the true statement Thus,is a solution of the equationWe also say that satisfiesthe equation because whenwe substitute for a true statement results.The set of all such solutions is calledthe equation’s solution set. For example, the solution set of the equationis because is the equation’s only solution.