Question 156696
Consecutive odd integers are integers that are odd and are next to one another. So numbers like 1,3,5,7,etc are consecutive odd integers. Algebraically, they follow the form {{{2x+1}}}, {{{2x+3}}}, {{{2x+5}}}, etc. where "x" is any integer.



Also, because "six more than nine times the first integer is five times the second integer", this translates to {{{9(2x+1)+6=5(2x+3)}}} where {{{2x+1}}} is the first number and  {{{2x+3}}} is the second number






{{{9(2x+1)+6=5(2x+3)}}} Start with the given equation.



{{{18x+9+6=10x+15}}} Distribute.



{{{18x+15=10x+15}}} Combine like terms on the left side.



{{{18x=10x+15-15}}} Subtract {{{15}}} from both sides.



{{{18x-10x=15-15}}} Subtract {{{10x}}} from both sides.



{{{8x=15-15}}} Combine like terms on the left side.



{{{8x=0}}} Combine like terms on the right side.



{{{x=(0)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}.



{{{x=0}}} Reduce.



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{{{2x+1}}} Now move onto the expression for the first number



{{{2(0)+1}}} Plug in {{{x=0}}}.



{{{0+1}}} Multiply {{{2}}} and {{{0}}} to get {{{0}}}.



{{{1}}} Combine like terms.



So the first number is 1.




{{{2x+3}}} Now move onto the expression for the second number



{{{2(0)+3}}} Plug in {{{x=0}}}.



{{{0+3}}} Multiply {{{2}}} and {{{0}}} to get {{{0}}}.



{{{3}}} Combine like terms.



So the second number is 3.



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Answer:



So the two numbers are 1 and 3



Check:


{{{9(1)+6=5(3)}}}



{{{9+6=15}}}



{{{15=15}}} works.