Solving inequalities

[Math_Junkie]

How close to -4 do we have to take x so that the following inequality is satisfied? (Give the largest possible value.)

1/(x+4)[sup:2211f98y]6[/sup:2211f98y] > 1,000,000

| x - (-4) | < ?

I thought the answer was -3.9 but turns out I'm wrong. Any help?

 

[Deleted member 4993]

How close to -4 do we have to take x so that the following inequality is satisfied? (Give the largest possible value.)

1/(x+4)[sup:3nqmi7iw]6[/sup:3nqmi7iw] > 1,000,000

| x - (-4) | < ?

Take sixth root of the equation (1)

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[Math_Junkie]

[quote="Math_Junkie":1yired9d]How close to -4 do we have to take x so that the following inequality is satisfied? (Give the largest possible value.)

1/(x+4)[sup:1yired9d]6[/sup:1yired9d] > 1,000,000

| x - (-4) | < ?

Take sixth root of the equation (1)

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.[/quote:1yired9d]

Sure, here's my work:

1/(x + 4)[sup:1yired9d]6[/sup:1yired9d] > 1,000,000
1/(x + 4) > 10
1 > 10(x + 4)
1 > 10x + 40
-39 > 10x
x < -3.9 / 10
x < -3.9

 

[Deleted member 4993]

[quote="Subhotosh Khan":d86999ky][quote="Math_Junkie":d86999ky]How close to -4 do we have to take x so that the following inequality is satisfied? (Give the largest possible value.)

1/(x+4)[sup:d86999ky]6[/sup:d86999ky] > 1,000,000

| x - (-4) | < ?

Take sixth root of the equation (1)

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.[/quote:d86999ky]

Sure, here's my work:

1/(x + 4)[sup:d86999ky]6[/sup:d86999ky] > 1,000,000
1/(x + 4) > 10

|(x+4)| < 1/10

1 > 10(x + 4)
1 > 10x + 40
-39 > 10x
x < -3.9 / 10
x < -3.9[/quote:d86999ky]

 

[Math_Junkie]

So -4.1 < x < -3.9, x cannot equal 4?

In my program it says, | x - (-4) | < ?

My answer was | x - (-4) | < -3.9 and I'm not understanding why it's wrong.

 

[BigGlenntheHeavy]

How close to 3 do we have to take x so that the following inequality is satisfied? (give the largest possible value)

x > 3

Well how about 3.00001 or 3.000001 or 3.0000001 or ad nauseum.