Module 10 Guess, Try and CheckThis module discusses the definition of the solution set of a first degreeequation or inequality in one variable.It also deals with the representation of thesolutions of equations and inequalities on a number line. Equations andinequalitiesareuseful inindustryandinotherfieldslikescience. Thus, it isimportant toknowthedifferent methodsofsolvingequationsandinequalities.Some of these methods are discussed in this module.There are five lessons in this module.Lesson 1 Solving Linear Equations in One VariableLesson 2 Solving Linear Inequalities in One variableLesson 3 Solving Linear Equations and Inequalities on a Number LineLesson 4 Solutions of Linear Equations and Inequalities from Replaement SetLesson ! "et#ods of Solving Linear Equations and Inequalities in One VariableAfter working on this module, you are epected to! define the solution set of a first degree equation or inequality in one variable illustrate the solution set of equations and inequalities in one variable on a number line find the solution set of simple equations and inequalities in one variable from a given replacement set find the solution set of simple equations and inequalities in one variable byinspection1What you are expected to learnWhat this module is all about "ultiple #hoice.#hoose the letter of the correct answer.$. %hich of the following statements is false&a. 'x ( ',ifx ( $b. ) * x ( +,,ifx ( +$-c. .x ( $-, if x ( /d. x 0 +',if x ( '.. %hich equation is true if b ( .&a. 'b ( , c.$ 1 .b ( ' b. )b 1 $ ( - d.b ( 'b 1 $'. %hat equation has 2-3 as solution set&a.y * $ ( - c.y 0 -b.y + $ ( +$ d.y 4 $). %hat is the solution set of 'y * $ ( $-&a.2.3 b.2'3 c.2)3 d.2535. 6etermine the open sentence with 1$ as one of its solutions.a. 0 $ c. 4 +.b. 4 $ d. 0 - ,. %hich of the following equations represents the graph below& +. a. d 1 $ ( ' c. d 1 $ 0 'b. d * $ ( +$ d. d * $ 4 + $2What to do before (Pretest) 7. Illustrate the graph of v ( 8. a.+. +$b. +$ -c. - $d. $ ./. %hich of the following graphs illustrates the solution set of a 0 5&a. 5b. 5c. 5 d. 53

9. %hich of the graphs drawn below represents the solution set of the inequality s + . 4 -&a. .b. .c. . d. .$-.6etermine which sentence has $/ as the onl$ solution.a. b * . ( +$, c.r $/b. h:. ( 9 d.w $/$$. %hat is the solution set of .; * $ ( $ taken from the replacement set 2+., +$, -, $3& a.2 +. 3 b.2 + $ 3c.2 - 3 d.2 $ 3$.. %hat sentence is satisfied by all elements of the set 2+$, -3&a.,m 1 $ ( 7 c. 5x * ' ( ) * 'b.1. 0 t 1 ' d. b 1 5 4 +)$'. ecall that a first degree equation or inequality in one variable may be trueor false when replaced by a specific value.The valueCsD that would replace thevariable willbe taken from a replaement set. Aou should always rememberthat the solution set taken from a given replacement set is not neessaril$thesolution set of an equation or inequality.%e consider the following eamples.Eample $.emember that To solve an equation:inequality using1% (uess&and&)#e'%e guess and substitute some values to see if a true equation:inequalityresults.The value:s which make:s the equation:inequality true is the solution of the equation:inequality.2% )over&up%e over&up the term with the variable and solve for value:s which will make the resulting open sentence true.3% *or'ing +a',ards%e reverse the procedure in the given equation:inequality.Self+#heckI. Solve the following equations by inspection.%& .' ( 7 * -)& $)) ( $.a ).) * .p ( $-*& 8 h ( 9 5./, ( b 1 .II. >epresent the solution sets of the equations given in I on a number line.III. =ind the solution set of the following inequalities by inspection and graph the solution set on a number line.%& t * 7 4 / )..x 1 . 0 ,)& .a , 5.'y +9*& 8 b 0 )21 Nosttest "ultiple #hoice.#hoose the letter of the correct answer.$. The following are true EO#ENTa. $9 1 x ( .5,if x ( , c..$ 1 )m ( $',if m ( .b. 7a * . ( $,,ifa ( . d.15 ( +b * ),ifb ( 9.. %hich of the following is true ifa ( +$&a. a 1 7 0 - c.'a +$b. .a 4 - d.. * a +''.%hat equation has 2+$3 as solution set&a.y * $ ( - c.y 0 +$b.y + $ ( +$ d.y 4 +$).6etermine the open sentence with +. as one of its solutions.a. 0 $ c. 4 +.b. 4 $ d. 0 +.5.%hich of the following equations represents the graph below& ,c. $ * 5 ( +$$ c.. * 5 ( $$d. $$ ( / + 5 d.0 1 5 ( +$$22 ,.Illustrate the graph of a ( +8. a.+. +$b. +$ -c. - $d. $ .7.>epresent the graph below by an open sentence. +5a. x ( +5 b.x 0 +5c.x +5 d.x +5/.%hich of the following graphs illustrates the solution set of a .&a. .b. .c. . d.23 .9.