Continuation of picture 2.6. Use interval notation or set notation to write the final answer. [-1,2] refer to the review sectionx + 1forsolvingdenominators)unlikex - 23. Set the numerator and Numerator:denominator equal to zeroand solve. The values youx +1 = 0x = -1critical Denominator:getvalues.arecalledx - 2 = 0x = 24. Plot the crițical values on anumber line, breaking thenumber line into intervals.5. Substitute critical values3八-1to the inequality todetermine if the endpointsx - 2when x = -1of the intervals in thesolution should be--1-1 - 23人-1-3included or not.-1 <-1(x = -1 is included inthe solution)when x = 23.<-12 2<-1undefined <-1 X(x = 2 is not included inthe solution)5. Select test values in eachinterval and substitutethose values into the-11inequality.when x = -2Note:3<-1-2 – 23If the test value makes theinequality true, then the-4S-1X falseentire interval is a solutionto the inequality.when x = 0If the test value makes the3<-1inequality false, then theentire interval is not a0- 23<-1 vtruesolution to the inequality.-2when x = 33S-13 - 23 <-1 X false3. 1. Solve example 2 of the rational equation by following the given steps.Example 2Example 1111x- 3x2 - 25x² - 1x- 1%3DRational Equationx+5(x- 5)1. Find the LeastLCD:Common Denominator(x+5)(x – 5)(LCD).2. Multiply both sides ofthe equation by its the1+x-3(x +5)(x – 5)[%3Dx2-25x+51LCD.(x-5)3. Apply the DistributiveProperty and thensimplify.(x - 3) + 1(x - 5) = 1(x + 5)x - 3 +x - 5 = x +5%3Dsimplify:2x -8 = x + 52x - x = 8 +5x = 134. Find all the possiblex = 13values of x.5. Check each value byChecking:x- 311substituting into originalequation and reject anyextraneous root/sx2 - 25x +5(x – 5)13 311132 2513 +5 (13 - 5)-1011169 251018 81 1= -14418 810 +8 1= -1448.1 1%3D8.8Note: No extraneous root2. Solve example 2 of rational inequality. You can refer to example 1 for the guidedsteps.Example 13<-1Example 23x + 1Rational Inequalityx - 2X - 11. Put the rational inequalityin general form.3.+1<0R(x)> 0Q(x)X - 2where > can be replacedby <,< and >Write the inequality into asingle rational expressionon the left side. (You can3+ 1(x – 2)|x - 2112

We need to solve example 2 by following steps from example 1. As per our guidelines we can not solve…

1. Solve example 2 of the rational equation by following the given steps. Example 2 Example 1 1 1 x-3 1 1 Rational Equation %3D x2 - 25 x +5 (x- 5) x2 - 1 X-1 1. Find the Least LCD: Common Denominator (x +5)(x – 5) (LCD). 2. Multiply both sides of the equation by its the x-3 (x + 5)(x - 5)[?=25 x+5 LCD. (x-5) 3. Apply the Distributive Property and then simplify. (x - 3) + 1(x - 5) = 1(x + 5) x- 3+x-5 = x + 5 simplify: 2x-8 = x + 5 2x -x = 8+5 x = 13 4. Find all the possible values of x. x = 13 5. Check each value by Checking: substituting into original equation and reject any extraneous root/s x-3 1 1 %3D x2 -25 x +5 (x - 5) 13 - 3 1 1 132 - 25 13 +5 (13 – 5) 10 1 169 - 25 10 18 1 %D 144 18 10 +8 1 144 8. 1 1 8. Note: No extraneous root 8. Solve example 2 of rational inequality You can refor 118118 II