document.write( "Question 27811: 1.2x-10+13+1=5x+11
\n" ); document.write( "2.8x/3-3=2x/3+15
\n" ); document.write( "3.12x/5+5=29-3x/5
\n" ); document.write( "4.2x/5-2=12x/5+11
\n" ); document.write( "5.3x/7-4=24x/7+8 \n" ); document.write( "
Algebra.Com's Answer #15200 by sdmmadam@yahoo.com(530)\"\" \"About 
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1.2x-10+13+1=5x+11
\n" ); document.write( "-10+13+1-11= 5x - 2x (taking 2x to the right and bringing 11 to the left)
\n" ); document.write( "(change side then change sign)
\n" ); document.write( "(-10-11)+(13+1) = 3x (by additive commutativity and associativity)
\n" ); document.write( "-21+14 =3x
\n" ); document.write( "-7 = 3x
\n" ); document.write( "(-7)/3 = x (dividing both the sides by 3)
\n" ); document.write( "Therefor x = -7/3
\n" ); document.write( "Verification: Put x=-7/3 on the LHS. You get (-14/3) +4 = (-14+12)/3 = -2/3
\n" ); document.write( "RHS = 5x+11 = 5X(-7/3) + 11 = (33-35)/3 = -2/3 LHS
\n" ); document.write( "Therefore x = -7/3 is right
\n" ); document.write( "Note: The advantage of commutativity is you can pluck a term from some position on a side and place it in some other position on the same side along with the sign of course.(transplantation!)\r
\n" ); document.write( "\n" ); document.write( "2.8x/3-3=2x/3+15
\n" ); document.write( "(8x/3- 2x/3) = 15+3 (transposing, that is changing side)
\n" ); document.write( "(8x-2x)/3 = 18
\n" ); document.write( "6x/3 = 18
\n" ); document.write( "2x =18
\n" ); document.write( "x=9
\n" ); document.write( "Answer: x = 9
\n" ); document.write( "Verification: for x=9 LHS = 21 =RHS\r
\n" ); document.write( "\n" ); document.write( "3.12x/5+5=29-3x/5
\n" ); document.write( "12x/5+3x/5 = 29 - 5
\n" ); document.write( "(12x+3x)/5 = 24
\n" ); document.write( "15x/5 = 24
\n" ); document.write( "3x=24
\n" ); document.write( "x = 24/3 = 8
\n" ); document.write( "x=8
\n" ); document.write( "Verification: LHS = (96/5+5) = 121/5
\n" ); document.write( "RHS = (29-24/5) = (145-24)/5 = 121/5 = LHS
\n" ); document.write( "Therefore x = 8 is correct\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4.2x/5-2=12x/5+11
\n" ); document.write( "2x/5 -12x/5 = 11 +2
\n" ); document.write( "(2x-12x)/5 = 13
\n" ); document.write( "(-10x)/5 = 13
\n" ); document.write( "-2x = 13
\n" ); document.write( "x = 13/(-2) = -13/2
\n" ); document.write( "x = -13/2
\n" ); document.write( "Verification: LHS = 2x/5-2 = -13/5 -2 = (-13-10)/5 = -23/5
\n" ); document.write( "RHS= 12x/5 + 11 = -78/5 +11 = (55-78)/5 = -23/5 = LHS
\n" ); document.write( "Therefore x = -13/2 is correct\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "5.3x/7-4=24x/7+8
\n" ); document.write( "3x/7 - 24x/7 = 8 +4
\n" ); document.write( "(3x-24x)/7 = 12
\n" ); document.write( "-21x/7 = 12
\n" ); document.write( "-(3X7x)/7 = 12
\n" ); document.write( "-3x = 12 (cancelling 7 in the nr and in the dr)
\n" ); document.write( "x = 12/(-3) = -4
\n" ); document.write( "Answer: x = -4
\n" ); document.write( "Verification: LHs = 3x/7-4 (3X(-4)/7 -4 = -12/7 -4 = (-28-12)/7 = -40/7
\n" ); document.write( "RHS = 24x/7+8 = 24X(-4)/7 + 8 = -96/7 + 8 = (56-96)/7 = -40/7 = LHS
\n" ); document.write( "Therefore x = -4\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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