Solve the inequality $$\(|2 x-1|<3|x+1|\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s21_qp_32 Year：2021 Question No：1
Answer:
State or imply non-modular inequality \((2 x-1)^{2}<3^{2}(x+1)^{2}\), or corresponding quadratic equation
Form and solve a 3-term quadratic in \(x\)
Obtain critical values \(x=-4\) and \(x=-\frac{2}{5}\)
State final answer \(x<-4, x>-\frac{2}{5}\)
Alternative method for Question 1
Obtain critical value \(x=-4\) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \(x=-\frac{2}{5}\) similarly
State final answer \(x<-4, x>-\frac{2}{5}\)
Form and solve a 3-term quadratic in \(x\)
Obtain critical values \(x=-4\) and \(x=-\frac{2}{5}\)
State final answer \(x<-4, x>-\frac{2}{5}\)
Alternative method for Question 1
Obtain critical value \(x=-4\) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \(x=-\frac{2}{5}\) similarly
State final answer \(x<-4, x>-\frac{2}{5}\)
Knowledge points:
3.1.1 understand the meaning of |x| , sketch the graph of y = |ax +b| and use relations such as and |x -a| < b for non-linear functions f are not included.)
Solution:
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