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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

14.8 含绝对值的不等式 Inequalities Involving Absolute Values

14.8 Inequalities Involving Absolute Values 含绝对值的不等式


Solve the inequalities
解下列不等式

 

(1) |2x + 1| < 3
Answer:
-2 < x < 1
(2) |2x - 1| > 3
Answer:
x > 2 or x < -1
(3) |x^2 - 4| > 3
Answer:
x<-\sqrt{7} or -1<x<1 or x>\sqrt7
(4) |x - 1| > 2x + 1
Answer:
x < 0
(5) |2x^2- 1| > x + 1
Answer:
x < \frac{1-\sqrt{17}}{4}, -\frac{1}{2} < x < 0, x > \frac{1+\sqrt{17}}{4}
(6) |2x - 1| < x + 1
Answer:
0 < x < 2
(7) 2 |2x- 1| <x + 1
Answer:
\frac{1}{5}\ < x < 1
(8) \left|1-\frac{2x}{x+2}\right|\geq3
Answer:
-4 \leq x < -2, -2 < x \leq -1
(9) |2x^2 - 6x + 1| < x + 1
Answer:
0 < x < \frac{1}{2}, 2 < x < 3 \frac{1}{2}
(10) |x^2 + x| < |x^2 - 1|
Answer:
x < -1 , -1 < x < \frac{1}{2}

(11) |2x - |x + 1|| < 4
Answer:
-1\frac{2}{3} < x < 5

(12) |\sqrt{3-2x}-3|<4
Answer:
-23 < x \leq 1\frac{1}{2}