course Mth 158
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3. The domain of the variable in the expression x/x-4 is 4.
6. An equation of the form ax+b=0 is called a(n) LINEAR equation or an(n) FIRST DEGREE equation.
Solve equations
9. 7x = 21 x = 3
12. 6x + 18 = 0 x = -3
15. 1/3x = 5/12 x = 5/4
Solve
18. 2x + 9 = 5x x = -7
20. 5y + 6 = -18 - y 5y + 6 = -18 - y 6y/6 = -24/6 y = -4
__________________ =
+y - 6 -6 + y
23. 3 + 2n = 4n + 7 3 + 2n = 4n + 7
________________
-3 -3
________________________
2n = 4n + 4
-4n = -4n
_________________________
-2n/-2n = 4/-2 = n = -2 {-2}
26. 3(2-x) = 2x - 1 = 6-3x = 1x = 3x = 1x = 2x
29. 3/2x + 2 = 1/2 - 1/2x 2[3/2x + 2 = 1/2 - 1/2x] 3x + 4 = 1 - 1x
+1x - 4 = -4 + 1 x = -3/4
__________________
4x/4 = -3/4
32. ??
36. 0.9t = 1 + t = 0.9t = 1 + t
-t - t = t = -10
________________
-.1t/-.1 = 1/-.1
38. ??
41. 1/2 + 2/x = 3/4 4x(1/2 + 2/x) = 3/4 x 4
2x + 8 = 3x
2x + 8 - 2x = 3x - 2x 8 = x
44. (x+2)(x-3) = (x+3)^2
6(x+2)(x-3) = (x+3)6
(6x+12)(6x-18) = (6x + 18)
6(x+2)(x-3) is not the same as (6x+12)(6x-18). Multiplication by 6 does not distribute over multiplication. Multiplication distributes over addition.
-6 12 - 18 = -30
47. z(z^2 + 1) = 3 + z^3
z^3 + 2 = 3 + 2^3
z^3 + z-z^3 = 3+z^3-z^3
z = 3
50. ??
52. x/x^2-9 + 4/x+3 = 3/x^2-9 (x^2-9)x/x^2-9 + 4/x+3 x+ 4/x+3 = 3/x^2-9(x^2-9) = 3
55. 5/2x-3 = 3/x+5 (2x-3)(x+5)(5/2x-3) = (3/x+5)(2x-3) (x+5)5 = (3)(2x-3) = 5x+25 = 6x - 3 = 5x+25-6x = 6x-9-6x=
25-x = 9 25-x-25 = -9 - 25
-x = -34
-x/-1 = -34/1 = x = 34
58. 8w+5/10w-7 = 4w-3/5w+7
61. ??
64. x+1/x^2+2x - x+4/x^2+x = -3/x^2+3x+2
67. ??
70. 1 - ax = b, a does not equal 0 1 - ax = b
-1 -1 x = b-1/-a
___________________
ax/-a = b-1/-a
72. a/x + b/x = c, c does not equal 0 x[a/x + b/x = c] a+b/c = cx/c a+b/c = x
76. Find the number b for which x = 2 is a solution of the equation.
x + 2b = x - 4 + 2bx 2 + 2b = 2-4 + 2b(2)
2 + 2b = 2-4 + 4b
2 + 2b = -2 + 4b
2 - 2b = 2 - 2b 4/2 = 2b/2 = 2 = b
79. Mechanics F = mc^2/R for R RF = R(mv^2/R) RF = MV^2 You still have to divide both sides by F; you'll get R = M V^2 / F.
82. ??
85. An inheritance of $900,000 is to be divided among Scott, Alice, and Tricia in the following manner -- Alice is to receive 3/4 of what Scott gets, while Tricia gets 1/2 of what Scott gets. How much does each receive?
Scott - X Alive - 3/4x Tricia- 1/2x Total - $900,000
x + 3/4x + 1/2x = 900,000
9/4x = 900,000 x = 4/9 (900,000) x = 400,000
Scott receives $400,000 Alice receives $300,000 Tricia receives $200,000
90. ??
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I can see some of what you are doing, and your procedures appear valid. See my note(s). Let me know if you have questions.