In 2006 the median yearly family income was about $48,200 per year. suppose the average annual rate of change since then is $1240 per year. write and graph an inequality for the annual family incomes y that are less than the median for x years after 2006.

First of all these type of questions are logical so we should look the sequence of numbers and try to find a relation between them

So what we see

First number =4. 2nd=9 3rd=17 . 4th =35. 5th is 69 then X then277

As you can see if we take the first number which is 4 and multiply it by2 and then add one we get 9

4×2+1=9

Now we take 2nd number that is 9

Now multiply 9 by 2 and substraction 1from the result we get 17 which is 3rd number

9×2–1=17

Now we take 17 multiply it by two and add one we get 35

So here we get the idea of what is going on with those numbers

‘To get the next term we have to multiply the number by 2 and then add and substract alternately '

So here we get the sutra (method).

So now it is easy to find the value of X

The number before X is 69

So now multiply it by 2 and then add 1

That is

69×2+1=139

So the value of X is 34

Now if you want to check it's correct or not then multiply it by two and substract one as we have to add and subtract one alternately so here we go

139×2–1=277

Which is the number .so our method is 100% correct.

PEACE!!

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