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{SECT 0 {PARA 0 "" 0 "" {TEXT 257 50 "High School Modules > Algebra by
 Gregory A. Moore " }}{PARA 3 "" 0 "" {TEXT -1 4 "    " }{TEXT 256 24 
"Solving Linear Equations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 45 "Learning the steps to solve linear equations." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 153 "[Direct
ions : Execute the Code Resource section first. Although there will be
 no output immediately, these definitions are used later in this works
heet.]" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 4 "Code" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 9 "restart; " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 81 "AddBothSides  :=  proc( expr, a )\n    lhs(expr) + a \+
= rhs( expr) + a; \n end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 104 "MultBothSides  :=  proc( expr, a )\n    simplify(lhs(expr) * \+
a) = simplify( rhs( expr) * a) ; \n end proc:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 112 "SimplifyBothSides := proc( expr )\n    simplify
( factor( lhs(expr) )) = simplify( factor( rhs(expr) ));\nend proc:" }
}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Example 1" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "17*x - 5 = 29;" }}}{PARA 0 "" 0 "" {TEXT -1 
113 "\nLets get rid of the number term, -5,  on the same side as the x
 term, by adding its opposite, +5 \nto both sides." }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "AddBothSides( %, 5);" }}}{PARA 0 "" 0 "" 
{TEXT -1 53 "\nNow, we multiply both sides by the reciprocal of 17." }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "MultBothSides( %, 1/17);" }
}}{PARA 0 "" 0 "" {TEXT -1 80 "\nWe are done. We found the answer. Map
le can also solve the problem in one step." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 27 "solve( 17*x - 5 = 29,  x) ;" }}}}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 9 "Example 2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "1/7*x+1 = 1/4*x-35;" }}}{PARA 0 "" 0 "" {TEXT -1 109 "\nLets first
 clear the denominators by multiplying both sides by the LCM, 28,  of \+
the \n denominators, 7 and 4." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "MultBothSides( %, 28);" }}}{PARA 0 "" 0 "" {TEXT -1 68 "\nNow le
ts get rid of the smaller x term, so only one x term remains." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "AddBothSides( %, -4*x);" }}}
{PARA 0 "" 0 "" {TEXT -1 152 "\nWe still have two purely number terms,
 28 and 980. Lets eliminate the one, -980, on the same side as the \nx
 term, by adding its opposite to both sides." }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 22 "AddBothSides( %, 980);" }}}{PARA 0 "" 0 "" {TEXT 
-1 87 "\nThere is one final step : to change 3x into x by multiplying \+
y by the reciprocal, 1/3." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"MultBothSides( %, 1/3);" }}}{PARA 0 "" 0 "" {TEXT -1 79 "\nWe are don
e. We found he answer. Maple can also solve the problem in one step." 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve( 1/7*x+1 = 1/4*x-35,
  x) ;" }}}{PARA 0 "" 0 "" {TEXT -1 186 "\nNote that we added to both \+
sides twice in a row. First we added -4x, then we added 980. Why not \+
\ndo both steps at once? Here is how this problem would look if we spe
d it up in this way." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "1/7*
x+1 = 1/4*x-35;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "MultBoth
Sides( %, 28);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "AddBothSi
des( %, -4*x + 980 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Mu
ltBothSides( %, 1/3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 9 "Example 3" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "(3/5)*(x - 7/3) = (1/9)*x + 3*(4*x - 5/2);" }}}{PARA 
0 "" 0 "" {TEXT -1 236 "Note that Maple automatically distributes and \+
combines like terms on both sides. \n\nHowever, there is still more to
 do. Lets first clear the denominators by multiplying\nboth sides by t
he LCM, 90,  of the various denominators, 2, 5 and 9." }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "MultBothSides( %, 90);" }}}{PARA 0 "" 0 "
" {TEXT -1 68 "\nNow lets get rid of the smaller x term, so only one x
 term remains." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "AddBothSid
es( %, -54*x);" }}}{PARA 0 "" 0 "" {TEXT -1 147 "\nWe still have two p
urely number terms. Lets eliminate the one, -675, on the same side as \+
the \nx term, by adding its opposite, +675, to both sides." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "AddBothSides( %, 675);" }}}{PARA 0 
"" 0 "" {TEXT -1 93 "\nThere is one final step : to change 1036x into \+
x by multiplying y by the reciprocal, 1/1036." }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "MultBothSides( %, 1/1036);" }}}{PARA 0 "" 0 "" 
{TEXT -1 80 "\nWe are done. We found the answer. Maple can also solve \+
the problem in one step." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "
solve( (3/5)*(x - 7/3) = (1/9)*x + 3*(4*x - 5/2),  x) ;" }}}}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 9 "Example 4" }}{PARA 0 "" 0 "" {TEXT -1 122 
"These same methods will be used to solve more advanced problems, late
r. For example, if we have\nan expression like this :\n" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "3/(x-2) + 5/x = 7;" }}}{PARA 0 "" 
0 "" {TEXT -1 88 "\nWe can multiply both sides by the LCM of the algeb
raic expressions in the denominators." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "MultBothSides( %, (x-2)*x );\n" }}}{PARA 0 "" 0 "" 
{TEXT -1 98 "\nIn this case, we can move everything to one side by add
ing the opposite of (8x-10) to both sides." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "AddBothSides( %, -(8*x -10) );" }}}{PARA 0 "" 0 "" 
{TEXT -1 28 "\nWe can simplify both sides." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "SimplifyBothSides(%);" }}}{PARA 0 "" 0 "" {TEXT -1 
98 "\nSince this is not a linear equation, we need to use other method
s. We'll discuss this more later." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "solve(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 259 35 "\n         \251 2002 Wa
terloo Maple Inc" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0" 8 }
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