Unit 1a - Algebra Review

Solving Equations

100

5x + 4x - 15 = 12

9x = 27

x = 3

200

13x + 70 = 10x + 106

3x = 36

x = 12

300

-2(x - 7) = 9 + 4(x + 4)

(fraction answer)

-11 = 6x

x = -11/6  or  -1  5/6

400

20(2x + 1) + 100 = 15(x + 3)

40x - 15x = 45 - 120

25x = -75

x = -3

500

-12x + 9 - 4x = -10 + 9x + 2 + 9x

(fraction answer, reduce, no decimals)

-16x + 9 = 18x - 8

17 = 34x

x = 17/34  =  1/2

Equations w/ Fractions

100

1/3(6x - 24) = 32

2x - 8 = 32

2x = 40

x = 20

200

1/4 x + 30/8 = 3/2 x

(clear the fractions first)

2x + 30 = 12x

30 = 10x

x = 3

300

(2x + 1) / 3 = x + 7

2x + 1 = 3x + 21

x = -20

400

x - 4/7 = 12/77

clear the fraction, reduce your final answer)

77x - 44 = 12

77x = 66

x = 66/77  =  6/7

500

29/18 + 1/2x = -5/3(x + 1/3)

29 + 9x = -30(x +1/3)

39x = -39

x = -1

+ & - polynomials

100

Sum of (3x²+8x-10) and (4x²+9x+1)

7x² + 17x - 9

200

Difference between (-10x² + 2x -17) and (10x² -13x)

-10x² - 10x² +2x - (-13x) - 17

-20x² +15x - 17

300

Difference between (5x³ + 45x - 1) and (8x³ - 5x + 18)

-3x³ +50x - 19

400

(8x² - 3x + 10) + (-3x² - 6x -7)

5x² - 9x + 3

500

(6x² - 7x + 1) - (9x² + 8x -6)

-3x² - 15x +7

x polynomials

100

12(4x - 7)

48x - 84

200

Multiply: (x + 4)(x - 6)

x² - 6x + 4x - 24

x² - 2x - 24

300

(3x - 8)(x + 5)

3x² + 15x - 8x - 40

3x² + 7x - 40

400

(4x - 9)(-x - 7x + 10)

-4x² - 28x² + 40x +9x + 63x - 90

-32x² + 112x - 90

500

1/2(x + 60)(x³ + 6x² - 4)

1/2x³ + 3x³ - 2x + 30x³ + 180x² -120

33 1/2 x³ + 180x² - 2x - 120

Complex #s

100

i^{2  =} 

-1

200

i⁴ = 

i²*i²  =  (-1)*(-1) =   1

300

2i + 9i - 15 - 14

(put in standard form)

-29 + 11i

400

7i(4 + 3i) + 6

(write in standard form)

28i + 21i² + 6

-21 + 6 + 28i

-15 + 28i

500

-3i(-14i + 8) + 4i - 12i²

42(-1) - 24i + 4i -12(-1)

-42+12 -24i+4i

-30 - 20i