SOLUTION: Four times the sum of a number and 6 is at least 6 times the same number less 14.for what numbers is this true?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Four times the sum of a number and 6 is at least 6 times the same number less 14.for what numbers is this true?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 740097: Four times the sum of a number and 6 is at least 6 times the same number less 14.for what numbers is this true?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
EXPLANATION OF THE INEQUALITY SET-UP:
(Understand the explanation, but do not include in your homework, unless you are sure the teacher wants to see all of it)
x= the number
x%2B6= the sum of the number and 6
4%2A%28x%2B6%29= four times the sum of the number and 6

6x= 6 times the number
6x-14= 6 times the number less 14

4%2A%28x%2B6%29 is at least 6x-14 means that
4%2A%28x%2B6%29 is equal to or greater than 6x-14
We write that as
4%2A%28x%2B6%29%3E=6x-14

THE SOLUTION:
4%2A%28x%2B6%29%3E=6x-14
4x%2B24%3E=6x-14 (after applying the distributive property on the left side)
24%3E=6x-4x-14 (after subtracting 4x from both sides)
24%2B14%3E=6x-4x (after adding 14 to both sides)
38%3E=2x (after performing indicated)
Then dividing both sides by 2, you get:
19%3E=x or highlight%28x%3C=19%29
(You may want to show less steps and explanations in the solution, according to what the teacher expects from you)