Solve inequality 4 / x + 1 is greater than or equal to x + 1!

Solve inequality 4 / x + 1 is greater than or equal to x + 1!

In other words, if the denominator x (x + 1) is less than or equal to 0 (x + 1) and less than 0 (x + 1) - 1 (x + 4), then the denominator x (x + 1) is less than or equal to 0 (x + 1) and less than or equal to 0 (x + 1) - 1 (x + 4)

Find the value of negative integer x which satisfies the inequality x + 2 greater than or equal to 2 / x + 4 + 6 / X-9 and 6 - (4 / X-2 + 3 / 2) greater than or equal to 6 / X

First
Double six on both sides
6x+12>=3x+12+x-9
6x-3x-x>=12-9-12
x>=-9/2
the second
Take 12 on both sides
72-3x+6-8>2x
5x

Solving inequality 1 / x-4 less than or equal to 1-x / 4-x

1/（X-4）≤（1-X）/（4-X）
1/（X-4）-（1-X）/（4-X）≤0
1/（X-4）+（1-X）/（X-4）≤0
（2-X）/（X-4）≤0
2≤X＜4

1,|1/2x+1|>=2、2,|5x-4|

|1 / 2x + 1 | > = 2 is equivalent to 1 / 2x + 1 is greater than 2, 1 / 2x + 1 is less than - 2, the rest is the same

Inequality 5x

Inequality 5x

What is the positive integer solution of inequality 2x-3 greater than or equal to 5x-10

2x-3 greater than or equal to 5x-10
2x-3>5x-10
3x

【1】 (3x-7) / 5 ＜ (X-2) / 2 [2] x / 4 - (2x-1) / 12 ≥ 1 / 6 - X / 3 solution inequality

【1】（3x-7）/5＜（x-2）/2
2(3x-7)＜5(x-2)
6x-14＜5x-10
6x-5x＜-10+14
x＜4
【2】 x/4-（2x-1）/12≥ 1/6 - x/3
3x-2x+1≥2-4x
x+4x≥2-1
5x≥1
x≥1/5

Inequalities 3 (x minus 3) less than or equal to 9 minus (x plus 6) and 4 plus x greater than 4x minus 17
After 9:00 on March 22

3(x-3)≤9-(x+6) (1)
4+x﹥4x-17 (2)
Solution (1)
3x-9≤9-x-6
3x+x≤9-6+9
4x≤12
x≤3
Solution (2)
x-4x﹥-17-4
-3x﹥-21
x﹤7
Therefore, the solution of the system of inequalities is x ≤ 3

Find the inequality X / 2 + X / 6 + 1 / 12 + 1 / 20 +The solution set of 1 / N (n-1) > n-1

x/2+x/6+x/12+x/20+…… +x/(n-1)n=(1/2+1/6+1/12+1/20+………… +1/(n-1)n)x=(1/1*2+1/2*3+1/3*4+1/4*5+………… +1/（n-1）n)x=(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+………… +1/（n-1）-1/n)x=(1-1/n)x>n-1x*(n-1)/n>n-1x...

It is known that 1 * 2 / 1 = 1-2 / 1; 2 * 3 / 1 = 2 / 1-3 / 1...; (n-1) n / 1 = n-1 / 1 to find the solution set of inequality 2 / x + 6 / x + 12 / x +... + (n-1) n > n-1

As a friendly reminder, your numerator and denominator are reversed. Note that the denominator is written at the bottom right of the fraction line / for example, 2 / 3 is 2 / 3
x/2+x/6+x/12+...+x/(n-1)n>n-1
x×[1/2+1/6+1/12+…… +1/(n-1)n]＞n-1
x×[1-1/2+1/2-1/3+1/3-1/4+…… +1/(n-1)-1/n]＞n-1
(1-1/n)x＞n-1
(n-1)x/n＞n-1
x＞n