Solve the inequality $$\(2|3 x-1|<|x+1|\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s21_qp_31 Year：2021 Question No：1
Answer:
State or imply non-modular inequality \( 2^{2}(3 x-1)^{2}<(x+1)^{2} \), or corresponding quadratic equation, or pair of linear equations
Form and solve a 3-term quadratic, or solve two linear equations for \( x \)
Obtain critical values \( x=\frac{3}{5}\quad and\quad x=\frac{1}{7} \)
State final answer \( \frac{1}{7}\ < x<\frac{3}{5} \)
Alternative method for Question 1
Obtain critical value \( x=\frac{3}{5} \) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \( x=\frac{1}{7} \) similarly
State final answer \( \frac{1}{7}\ < x<\frac{3}{5} \)
Form and solve a 3-term quadratic, or solve two linear equations for \( x \)
Obtain critical values \( x=\frac{3}{5}\quad and\quad x=\frac{1}{7} \)
State final answer \( \frac{1}{7}\ < x<\frac{3}{5} \)
Alternative method for Question 1
Obtain critical value \( x=\frac{3}{5} \) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \( x=\frac{1}{7} \) similarly
State final answer \( \frac{1}{7}\ < x<\frac{3}{5} \)
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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