Question 167751


{{{332*abs(x-11)+17000=18700}}} Start with the given equation



{{{332*abs(x-11)=1700}}} Subtract 17,000 from both sides.



{{{abs(x-11)=5.12048}}} Divide both sides by 332 (this is an approximate value)




Break up the absolute value (remember, if you have {{{abs(x)=a}}}, then {{{x=-a}}} or {{{x=a}}})


{{{x-11=-5.12048}}} or {{{x-11=5.12048}}} Set the expression {{{x-11}}} equal to the original value 5.12048 and it's opposite -5.12048





Now lets focus on the first equation  {{{x-11=-5.12048}}}



{{{x=-5.12048+11}}}Add 11 to both sides



{{{x=5.87952}}} Combine like terms on the right side



So rounding to the nearest whole number, we get {{{x=6}}}



This means that 6 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000. 


So in 1986 (which is 6 years away from 1980), the population of 15-19 yr olds was 18,700,000.



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Now lets focus on the second equation {{{x-11=5.12048}}}




{{{x=5.12048+11}}}Add 11 to both sides



{{{x=16.12048}}} Combine like terms on the right side



So rounding to the nearest whole number, we get {{{x=16}}}




This means that 16 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000. 


So in 1996 (which is 16 years away from 1980), the population of 15-19 yr olds was 18,700,000.




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Answer:


So we got the solutions (after rounding to the nearest whole number) {{{x=6}}} and {{{x=16}}}. These solutions represented the number of years after 1980. 


So in 1986 and in 1996 the population of 15-19 year olds was 18,700,000