Equations and Inequalities

Linear

100

solution of the linear equation

2x+7=31

What is x=12?

200

Solution to linear equation

3+1/3x=5

What is 6?

300

Solution to

3x+11<6x+8

What is x>1?

400

Solution to

2(7x-3)ge12x+16

What is 

xge11

500

z/5=3/10z+7

What is z=-70?

Quadratic Equations

100

Solutions to

x²+x-12=0

What is x=3 and x=-4?

200

Solutions to

2x²+3x+1=0

What is 

x=-1/2

x=-1

300

Solutions to 4x²-x=0

What is x=0 and 

x=1/4

400

Solutions to 3+5z+z²=0

What is 

x=(-5+-sqrt13)/2

500

Solutions by completing the square

x²-4x+2=0

What is 

x=2+-sqrt2

Quadratic Inequalities

100

Solutions in interval notation of

x(2-3x)le0

(-infty,0]U[2/3,infty)

200

Solutions of x²+5x+6<0

What is (-3,-2)?

300

Solutions to 

x^2ge9

(-infty,-3] U [3,infty)

400

Solutions to 

-2<(x+1)/(x-3)

What is 

(-infty,5/3)U(3,infty)

500

Solutions to

x/2ge5/(x+1)+4

What is 

[-2,-1]U[9,infty)

Other Equations

100

The number of real solutions for 

x²-6x+1=0

(Hint: use discriminant)

What is 2?

200

Solve for b

a²+b²=c²

What is 

b=+-sqrt(c^2-a^2)

300

Solutions to

sqrt(5-x)+1=x-2

What is x=4 and x=1?

400

Four consecutive odd integers whose sum is 416

What are 101, 103, 105, and 107?

500

Solutions to x⁴-13x²+40=0

What is 

x=+-2sqrt2

x=+-sqrt5

Absolute Value

100

Solutions to

abs(2x)=3

What is 

x=+-3/2

200

Solutions to 

abs(3x+5)=1

What is 

x=-4/3

x=-2

300

absxle4

Solution in interval notation of

[-4,4]

400

Solution in interval notation of

abs(3x)<15

What is (-5,5)?

500

Solutions to

abs((x+1)/2)ge4

What is 

xge7

xle-9