SOLUTION: 1/b+4 is less than or equal to 10+1/b Solve for b

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Question 641087: 1/b+4 is less than or equal to 10+1/b
Solve for b
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28b%2B4%29+%3C=+10%2B1%2Fb...I guess you have this
1%2F%28b%2B4%29+%3C=+%2810b%2B1%29%2Fb...cross multiply
1b+%3C=+%2810b%2B1%29%28b%2B4%29
b+%3C=+10b%5E2%2B40b%2Bb%2B4
0+%3C=+10b%5E2%2B40b%2Bb-b%2B4
0+%3C=+10b%5E2%2B40b%2B4

0+%3C=+2%285b%5E2%2B20b%2B2%29....use quadratic formula and solve like equation

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-20+%2B-+sqrt%28+20%5E2-4%2A5%2A2+%29%29%2F%282%2A5%29+

x+=+%28-20+%2B-+sqrt%28+400-40+%29%29%2F10+

x+=+%28-20+%2B-+sqrt%28+360+%29%29%2F10+

x+=+%28-20+%2B-+18.9%29%2F10+

x+=+%28-20+%2B18.9%29%2F10+
x+=+-1.1%2F10+
x+=+-0.11+ ....your b

x+=+%28-20+-+18.9%29%2F10+
x+=+-38.9%2F10+
x+=+-3.89+ ....your b

check which one is right solution for 1%2F%28b%2B4%29+%3C=+10%2B1%2Fb
1%2F%28-0.11%2B4%29+%3C=+10%2B1%2F-0.11
1%2F2.9+%3C=+10-9.09
0.34+%3C=+0.91........true

1%2F%28-3.89%2B4%29+%3C=+10%2B1%2F-3.89
1%2F0.11+%3C=+10-0.26
9.09+%3C=+9.74........true

0.34+%3C=+0.91........true