Solve the inequality about X 2x minus 1 / X is greater than or equal to 1 Urgent

Solve the inequality about X 2x minus 1 / X is greater than or equal to 1 Urgent

Just now, someone asked that when 2x-1 > 0, that is, when x > 1 / 2, X ≥ 2x-1 gets x ≤ 1, so we take the intersection 1 / 2 < x ≤ 1. When 2x-1 < 0, that is, x < 1 / 2, X ≤ 2x-1 equals x ≥ 1, and the intersection is empty, so the final value is 1 / 2 < x ≤ 1

Solving quadratic inequality of one variable - x ^ 2-2x + 8 greater than or equal to 0

-x^2-2x+8≥0
x^2+2x-8≤0
The two roots of the equation x ^ 2 + 2x-8 = 0 are: x = - 4 and x = 2
So the solution of the inequality is: - 4 ≤ x ≤ 2
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System of inequalities x≥1 The sum of integer solutions of 1 − 2x > 3 (x − 7) is () A. 9 B. 10 C. 23 D. 6

Solving inequalities
x≥1
1 − 2x > 3 (x − 7), 1 ≤ x < 22
5，
The integer solution of X is 1, 2, 3, 4,
The sum of integer solutions is 1 + 2 + 3 + 4 = 10
Therefore, B

(2013 · Tai'an) inequality system x−3(x−1)≤7 The solution set of 2x + 4 > 3x is () A. -2＜x＜4 B. X ≥ - 4 C. -2≤x＜4 D. -2＜x≤4

x−3(x−1)≤7①
2x+4＞3x② ，
The results are as follows
x≥-2，
The results are as follows: 1
x＜4，
The solution set of inequality system is: - 2 ≤ x < 4,
Therefore, C

To solve the inequality group: 2x+7≥1-x，① 6-3 (1-x) > 5x, ②

By solving the inequality, X ≥ - 2 is obtained,
Solving the inequality (2) leads to x < 3
2，
The solution set of the original inequality system is - 2 ≤ x < 3
2，
Then the integer solution of the original inequality system is - 2, - 1, 0, 1
The sum of all integer solutions is - 2 + (- 1) + 0 + 1 = - 2

Solution inequality (1) (x + 7) / (3x's square + 2x + 5) is greater than 1 (2) (square of x-5x + 6) / (square of x-3x-4) is less than or equal to 0

[sorry, it's too late to read the topic]
1) (x + 7) / (3x squared + 2x + 5) is greater than 1
Because 3x 2 + 2x + 5
=3(x²+2/3x+5/3)
=3[(x²+2×1/3×x+1/9)+14/9]
=3[(x+1/3)²+14/9]＞0
So the original inequality becomes
x+7＞3x²+2x+5
3x²+x-2＜0
(3x-2)(x+1)＜0
①3x-1＞0,x+1＜0
That is, X ＞ 1 / 3, X ＜ - 1
unsolvable
②3x-1＜0,x+1＞0
That is, X ＜ 1 / 3, X ＞ - 1
The value of X is - 1 < x < 1 / 3
To sum up, the inequality solution set-1 < x < 1 / 3
2) (square of x-5x + 6) / (square of x-3 x-4) is less than or equal to 0
(x²-5x+6)/(x²-3x-4)≤0
(1) When x? - 3x-4 > 0
That is (x-4) (x + 1) > 0
X-4 > 0, x + 1 > 0 or x-4 < 0, x + 1 < 0
When x > 4 or x < 1
The original inequality is reduced to x 2 - 5x + 6 ≤ 0
(x-2)(x-3)≤0
①x-2≤0,x-3≥0
That is, X ≤ 2, X ≥ 3
unsolvable
②x-2≥0,x-3≤0
x≥2,x≤3
The value range of X is 2 ≤ x ≤ 3
Because x > 4 or x < 1
So x has no solution
(2) When x? - 3x-4 < 0
That is (x-4) (x + 1) < 0
X-4 > 0, x + 1 < 0 or x-4 < 0, x + 1 > 0
When x ＞ 4, X ＜ - 1 or X ＜ 4, X ＞ - 1
That is - 1 < x < 4
The original inequality is transformed into x 2 - 5x + 6 ≥ 0
(x-2)(x-3)≥0
①x-2≥0,x-3≥0
That is, X ≥ 2, X ≥ 3
X value range X ≥ 3
②x-2≤0,x-3≤0
x≤2,x≤3
X value range X ≤ 2
Because - 1 < x < 4
So x solution set-1 < x ≤ 2,3 ≤ x < 4
To sum up, the inequality solution set 1 < x ≤ 2,3 ≤ x < 4

Solving inequalities 3(x+1)＞5x+4 x−1 2≤2x−1 3 ．

3(x+1)＞5x+4①
x−1
2≤2x−1
3② ，
Solving the inequality (1) leads to X ＜ - 1
2, (2 points)
Solving the inequality ② gets x ≥ - 1, (4 points)
The solution set of inequality system is - 1 ≤ x ＜ - 1
2. (5 points)

Solve the inequality group: ① 3 (x -) - 1 ≤ x, 2 (4.5-x) ≤ 3-x and ② 5x-2 < 3 (x + 1), 1 / 2x-1 is greater than or equal to 7-3 / 2x Solving inequality system ① 3 (x -) - 1 ≤ x 2(4.5-x)≤3-x ②5x-2＜3（x+1） 1 / 2x-1 greater than or equal to 7-3 / 2x These are two equations

5x-2>3(x+1)
5x-2＞3x+3
5x-3x＞3+2
2x＞5
x＞2.5
1/2x-1

Integral solutions of the inequality group 3x + 2 greater than or equal to 5x-6 3-2x ≤ x + 2

3X+2≥5X-6
2X≤8
X≤4
3-2X≤X+2
3X≥1
X≥1/3
1/3≤X≤4
Integer solution x = 1.2.3.4

To solve the inequality group: 2x−6≤5x+6 3x＜2x−1

By solving the inequality, X ≥ - 4 is obtained,
By solving inequality 2, X ＜ - 1 is obtained,
So the solution set of inequality system is: - 4 ≤ x ＜ - 1