Unformatted text preview: Algebra, continued. 07' Finally, let us suppose that we must solve the equation for x, given that A = 6.8, Q = 0.37, and T = 3.5. Dividing through by A isolates the term involving 3: on the left:
2
0.5=r = I" (1 — 111‘) To remove x from the exponent and have it appear on the line, take the logarithm of both sides: 1110.? = In [W] New by the properties of logarithms
In 0.5" = x In 0.5
we then obtain xln0.5=lnl:Qz(_1;_1/ﬂ] Dividing both sides by In 0.5, we obtain an equation for x In [Q2(1 e llTl] Algalert'u. “windy A
In 0.5 x: Now we substitute values for Q, T, and A [0.372(1' — [/13]
in _ 6.8
x = In 0.5
_ In 0.0m '
In 0.5
$4.24
= —0.693
"we r . Am; rearrangement is accomplished by treating both sides of the equation in Table . ‘ Solution of First Degree Equations in One Unknown
Equation Operation
1. 5x = 4
x = 4/5 = 0.8 Divide both sides by S
2‘ 30 = 0.063
x
3.0:: = 0.063 Multiply both sides by x
x “—' 0.02l Divide both sides by 3.0
3. 3x = 4 — 5x
3:: = 4 Add 5x to both sides
X = 413 = 05 Divide both sides by 8
5 2
4. — = _
2x — l x + 4 .
50: + 4) = 2(B  l) ' Multiply both sides by (2.: 1)(x + 4): goo
5x + 20 = 4x — 2 Minute "1!: harm: «rtmt or: courtifs.
x + 20 = —2 Subtract 4:: from both sides
x = —22 Subtract 20 from both sides :
Table ' Conversion to Fits: Degree Equations
Equation Operation
‘21. x1” = 6 ,
x = 36 Square both sides
2. x2 = 1.0 x 10‘” iM‘" “iv
= 1.0 X 10:6 Extra? Squargrogt of both sides
3. 4:3 =32 x 10'“ “4'“ ‘1' w". m ‘ M“ "
x3 = 0.3 x 10““l = 8.0 x 10‘” Divide by 4
x = 2.0 X 10' Extract cube root of both sides. (uhI, 3 nob, :2. «at 04....“ mom), some sort}: 5T;= ‘iT._—1é,o :0 an identical manner (so as not to destroy the equality) until the desired tern" is isolated. E . ... M
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To solve for a, divide b by c. To solve for b, multiply both sides of the equation by c. axc=§xf ,5 To solve for c, multiply both sides of the equation by g. c:—
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To solve for b, multiply both sides of the equation by :
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1r c 1 z 6.. (1.) (b ' C) ' =d 1 To solve for b, ﬁrst multiply both sides of the equation by n. Then add c to both sides of the equation. I b—y’+/a/=dxa+c  b=(dxa}+c . i Whena: I.8,c=32,andde35, _
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 Fall '08
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