SOLUTION: Can you help me with this solution to the inequality, ? 1. b > 11.2 b= 2. x(7-x)>8 x= 3. 6 ≤ 6k k= Hope you guys get these! :D Thanks!

Algebra ->  Inequalities -> SOLUTION: Can you help me with this solution to the inequality, ? 1. b > 11.2 b= 2. x(7-x)>8 x= 3. 6 ≤ 6k k= Hope you guys get these! :D Thanks!      Log On


   

Question 407367: Can you help me with this solution to the inequality, ?
1. b > 11.2
b=

2. x(7-x)>8
x=
3. 6 ≤ 6k
k=

Hope you guys get these! :D
Thanks!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. +b+%3E+11.2+...b cold be any number greater than 11.2, like
b=+11.21, b=+11.22,...b=+11.3...and so on

2.
x%287-x%29%3E8
7x-x%5E2%3E8
7x-x%5E2-8%3E0...solve quadratic as it is equal to 0

7x-x%5E2-8=0
-x%5E2%2B7x-8=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A%28-1%29%2A%28-8%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-7+%2B-+sqrt%28+49-32+%29%29%2F%28-2%29+
x+=+%28-7+%2B-+sqrt%28+17+%29%29%2F%28-2%29+
x+=+%28-7+%2B-+%28+4.12%29%29%2F%28-2%29+

x1+=+%28-7+%2B+4.12%29%2F%28-2%29+
x1+=+%28-2.88%29%2F%28-2%29+
x1+=+1.44+
x2+=+%28-7+-+4.12%29%2F%28-2%29+
x2+=+%28-11.12%29%2F%28-2%29+
x2+=+5.56+

x%287-x%29%3E8.........plug in x1 and x2 to see what will be a solution for this inequality

x%287-x%29%3E8...1.44%287-1.44%29%3E8....1.44%285.56%29%3E8...8.0064%0D%0A%3E8
for x2+=+5.56+
5.56%287-5.56%29%3E8...5.56%287-5.56%29%3E8....1.44%281.44%29%3E8...2.0736%0D%0A%3E8...this is not a solution
so, your inequality will be true only if
x+=+1.44+


3. 6+%3C=+6k
6%2F6+%3C=+k
1+%3C=+k...k could be 1 and any number greater than 1