Solving Equations and Inequalities Review

Solving Quadratics

100

x^2=25

x=5 or x=-5

200

x^2+12x+20=0

x=-10 or x=-2

300

x^2-11x+24=0

x=8 or x=3

400

3x^2+15x-42=0

x=-7 or x=2

500

3x^2+10x-8=0

x=-4 or x=2/3

Rational Expressions

100

Solve for x

(x+3)/(2)+(x-1)/(6)=0

x=-2

200

Simplify

(x^2+5x+6)/(x^2-9)*(5x-15)/(x^2+6x+8)

5/(x+4)

300

2/(x+2)+4/(x-2)=(x-1)/(x^2-4)

x=-1

400

(x^2+3x-28)/(x^2+4x+4)div(x^2-49)/(x^2-5x-14)

(x-4)/(x+2)

500

Solve

(x+11)/(x^2-5x+4)=5/(x-4)-3/(x-1)

emptyset

Solving Radical Equations

100

sqrt(x-4)=3

x=13

200

sqrt(5x-3)=sqrt(4x-1)

x=2

300

sqrt(2x-1)+2=x

x=5

400

sqrt(3x-8)=x-4

x=8

500

(x-6)^(2/3)=16

x=70 or x=-58

Absolute Value Equations & Inequalities

100

abs(2x-3)=5

x=4 or x=-1

200

Write your answer in interval notation

abs(x-5)<=3

[2,8]

300

2abs(x-4)-5=7

x=10 or x=-2

400

Write your answer in interval notation

abs(2x+3)>7

(-infty,-5)cup(2,infty)

500

abs(x^2-3)=-x+3

x=-3 or x=0 or x=1 or x=2

Quadratic & Rational Inequalities

100

Write your answer in interval notation

x^2-4x+3>=0

(-infty,1]cup[3,infty)

200

Write your answer in interval notation

(x-5)/(x+2)<0

(-2,5)

300

(6-2x)/(x^2+4x+3)>0

(-infty, -3)cup(-1,3)

400

(x-4)/x>=3

[-2,0)

500

3x^2-7x>6

(-infty,-2/3)cup(3,infty)