# Example 12 study tip be sure to square both sides of

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Chapter 8 / Exercise 30
Intermediate Algebra
Mckeague Expert Verified
EXAMPLE 12Study TipBe sure to square both sidesof anequation. Do notsquare each term.Correct:Incorrect!A22x-1B2=x2-22A22x-1B2=1x-222
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Chapter 8 / Exercise 30
Intermediate Algebra
Mckeague Expert Verified
Step 4Check the proposed solutions in the original equation.98Chapter PPrerequisites: Fundamental Concepts of AlgebraCheck 1:Check 5:22x-1+2=x22x-1+2=x22#1-1+2122#5-1+2521+2129+251+213+25false3=1,true5=5,Thus, 1 is an extraneous solution.The only solution is 5, and the solution set is Check Point12Solve:2x+3+3=x.556.Exercise Set P.7Practice ExercisesIn Exercises 1–16, solve each linear equation.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.Exercises 17–26 contain rational equations with variables indenominators. For each equation,a.Write the value or values ofthe variable that make a denominator zero. These are the restric-tions on the variable.b.Keeping the restrictions in mind, solve theequation.17.18.19.20.21.22.23.24.4x+5+2x-5=32x2-252x+1-1x-1=2xx2-13x+3=52x+6+1x-232x-2+12=2x-12x-2=xx-2-28xx+1=4-8x+13x+4-7=-4x+41x-1+5=11x-13x5-x-32=x+23x+13=5-x+275+x-23=x+38x4=2+x-33x+14=16+2-x3x+36=38+x-5421x-12+3=x-31x+1231x-22+7=21x+5213x+14=12x-57x+4=x+163x+5=2x+132x-7=6+x5x-12x-102=3511x-16x-52=406x-3=637x-5=7225.26.In Exercises 27–42, solve each formula for the specified variable.Do you recognize the formula? If so, what does it describe?27.for 28.for 29.for 30.for 31.for 32.for 33.for 34.for 35.for 36.for 37.for 38.for 39.for 40.for 41.for 42.for In Exercises 43–54, solve each absolute value equation or indicatethe equation has no solution.43.44.45.46.47.48.49.50.51.52.53.54.In Exercises 55–60, solve each quadratic equation by factoring.55.56.57.58.59.60.3x2=12x5x2=20xx2= -11x-10x2=8x-15x2-13x+36=0x2-3x-10=0ƒ3x-2ƒ +4=4ƒ2x-1ƒ +3=3ƒx+1ƒ +6=2ƒx+1ƒ +5=34`1-34x`+7=102`4-52x`+6=183ƒ2x-1ƒ =212ƒ3x-2ƒ =14ƒ2x-3ƒ =11ƒ2x-1ƒ =5ƒx+1ƒ =5ƒx-2ƒ =7f2f=f1f2f1+f2f1f=f1f2f1+f2R11R=1R1+1R2f1p+1q=1fhA=2lw+2lh+2whIIR+Ir=ErS=C1-rSB=FS-VtS=P+PrtrS=P+PrtbA=12h1a+b2aA=12h1a+b2MP=C+MCpT=D+pmrC=2prPI=Prt1x-3-2x+1=8x2-2x-31x-4-5x+2=6x2-2x-8
Section P.7Equations99In Exercises 61–66, solve each quadratic equation by the squareroot property.61.62.63.64.65.66.In Exercises 67–74, solve each quadratic equation by completingthe square.67.68.69.70.71.72.73.74.In Exercises 75–82, solve each quadratic equation using thequadratic formula.75.76.77.78.79.80.81.82.Compute the discriminant of each equation in Exercises 83–90.What does the discriminant indicate about the number and type ofsolutions?83.84.85.86.87.88.89.90.In Exercises 91–114, solve each quadratic equation by the methodof your choice.91.92.
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