Maths

posted by .

How many integers satisfy the inequality
∣10(x+1)/(x^2+2x+3)∣≥1?

• Maths -

since x^2+2x+3 is always positive,

|10(x+1)| >= (x^2+2x+3)

Now, x+1 is either positive or negative
If x+1 is positive, |x+1| = x+1, and
10(x+1) >= x^2+2x+3
4-√23 <= x <= 4+√23
-.8 <= x <= 8.8
We started with x+1>=0, so every integer between -.8 and 8.8 works. There are 9 of them

If x+1 < 0, |x+1| = -(x+1) and we have
-10(x+1) >= x^2+2x+3
-6-√23 <= x <= -6+√23
-10.8 <= x <= -1.2
We started with x+1 < 0, so x < -1, and every integer between -10.8 and -1.2 works. There are 9 of those.

So, there are 18 integers that satisfy the inequality.

Similar Questions

1. algebra

Find the largest possible integer n such that there exists a non-constant quadratic polynomial f(x) with integer coefficients satisfying f(1)∣f(2),f(2)∣f(3),…f(n−1)∣f(n). Details and assumptions: ~For (possibly …
2. MATHS

Find the largest possible integer n such that there exists a non-constant quadratic polynomial f(x) with integer coefficients satisfying f(1)∣f(2),f(2)∣f(3),…f(n−1)∣f(n). Details and assumptions For (possibly …
3. Mathematics

Find the number of pairs of non-negative integers (n,m), such that 1≤n<m≤100, n∣m^2−1 and m∣n^2−1. Details and assumptions The notation a∣b means a divides b, or b=ka for some integer k.
4. Maths

Find the number of pairs of non-negative integers (n,m), such that 1≤n<m≤100, n∣m2−1 and m∣n2−1. Details and assumptions The notation a∣b means a divides b, or b=ka for some integer k.
5. Maths

We have 15 points {Ai} placed within the unit sphere. What is the maximum possible value of ∑1≤i<j≤15 ∣∣AiAj∣∣^2?
6. science

1 A ……... is a rectangular array of numbers that are enclosed within a bracket . horizontal set vertical matrix 2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is called….. …
7. Probability

Let T1,T2,…,Tn be i.i.d. observations, each drawn from a common normal distribution with mean zero. With probability 1/2 this normal distribution has variance 1, and with probability 1/2 it has variance 4. Based on the observed values …
8. probability

This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2. (figure belongs to "the science of uncertainty) …
9. probability

Let K be a discrete random variable with PMF pK(k)=⎧⎩⎨⎪⎪1/3,2/3,0if k=1,if k=2,otherwise. Conditional on K=1 or 2, random variable Y is exponentially distributed with parameter 1 or 1/2, respectively. …
10. Probability

This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2. Are X and Y independent?

More Similar Questions