Algebra Review

Simplify

100

(4-9i)(9+i) 

45-77i

200

2/(3+sqrt(x)) 

(6-sqrt(2)) / (9-x)

300

sqrt(75x⁹y⁴)

5x⁴y² sqrt(3x)

400

(-8w²⁷x^-3y⁶)^-1/3

yz¹⁰/x²

500

[(x²+x-6)/(x²-2x+1)] / [(x-2)/(x²-1)]

(x+3)(x+1) / ((x-1) 

Solving Equations

100

3  l x+4 l + 3 = 21

-10, 2 

200

9^x+1 = 27

x = 1/2

300

2x² = 5x+7

x = -1, x=7/2

400

50/x - 50/(x-8) = 4/x

x= - 92

500

2x - 5 = sqrt(x+20) 

x = 5

Solving Inequalities

100

l 3x - 1 l < 5

Interval notation

(-inf, -4] U [5, inf)

200

l x - 5 l + 7 > 4

Interval Notation

(-inf, inf) 

300

l 1 - 2x l > 0 

(-inf, -4] U [5, inf)

400

(x-3) / (2x+2) < 0 

(-1, 3) 

500

x² - 5x - 14 < 0

Interval Notation

[-2, 7]

Find

100

f(x) = (2x - 1) / (x - 4) 

Find the domain

x cannot equal 4 

200

f(x) = sqrt(3-x)

Find the domain in interval notation

(-inf, -3]

300

Find the distance between

(-1, 7) and (8, -4) 

sqrt(202)

400

f(x) = 3x - 1 

Find f(a+1) 

3a+2 

500

f(x) = x² + 4x +3

Find f(x) = 8

x = -5, 1

Miscellaneous

100

x²  -5x + 1 =0

Find the solutions

x = 5/2 + sqrt(21)/2

200

(x-1)² = -81

x = 1+ 9i

300

x⁴ - 5x² + 4=0 

x = +2, x = +1 

400

Find the vertex and axis of symmetry 

y = x²+5

(0, 5), x = 0

500

Find the LCD 

3/(7x⁵y⁷) + 1/(6x⁶y⁵)

42x⁶y⁷