SOLUTION: How would you put this word problem into numbers eleven less than twice a number is at most 25 and at least 15?

Question 558422: How would you put this word problem into numbers eleven less than twice a number is at most 25 and at least 15?
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
eleven less than twice a number is at most 25 and at least 15

Replace the word "eleven" by "11".

11 less than twice a number is at most 25 and at least 15

Replace the words "a number" by "x".

11 less than twice x is at most 25 and at least 15

Replace "twice x" by 2x

11 less than 2x is at most 25 and at least 15

Replace the words "11 less than 2x" by "2x-11" (You make 2x less by subtracting from it)

2x-ll is at most 25 and at least 15

Replace the words "is at most" by "≦" which means "(is) less than or equal to"

2x-ll ≦ 25 and at least 15

Replace the words "(is) at least" by "≧" which means "(is) greater than or equal to"

2x-ll ≦ 25 and ≧ 15

That means that 2x-ll ≦ 25 and 2x-ll ≧ 15
Change the inequality on the right by reversing sides and reversing the inequality:

That means that 2x-ll ≦ 25 and 15 ≦ 2x-11

Write the second one first and the first one second:

15 ≦ 2x-11 and 2x-ll ≦ 25

No need for the duplication of 2x-11, so write:

15 ≦ 2x-ll ≦ 25

That's the inequality. To solve it, add 11 to all three sides: 15+11 ≦ 2x-ll+11 ≦ 25+11 26 ≦ 2x ≦ 36 Divide all three sides by 2 13 ≦ x ≦ 18 In interval notation that's [13, 18] Edwin

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