Solve the inequality $$\(|3 x-a|>2|x+2 a|\)$$, where $$\(a\)$$ is a positive constant. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w21_qp_32 Year：2021 Question No：2
Answer:
State or imply non-modular inequality \((3 x-a)^{2}>2^{2}(x+2 a)^{2}\), or corresponding quadratic equation, or pair of linear equations or linear inequalities
Make reasonable attempt to solve a 3-term quadratic, or solve two linear equations for \(x\)
in terms of \(a\)
Obtain critical values \(x=5 a\) and \(x=-\frac{3}{5} a\) and no others
State final answer \(x>5 a, x<-\frac{3}{5} a\)
Alternative method for Question 2
Obtain critical value \(x=5 a\) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \(x=-\frac{3}{5} a\) similarly
State final answer \(x>5 a, x<-\frac{3}{5} a\)
Make reasonable attempt to solve a 3-term quadratic, or solve two linear equations for \(x\)
in terms of \(a\)
Obtain critical values \(x=5 a\) and \(x=-\frac{3}{5} a\) and no others
State final answer \(x>5 a, x<-\frac{3}{5} a\)
Alternative method for Question 2
Obtain critical value \(x=5 a\) from a graphical method, or by solving a linear equation or linear inequality
Obtain critical value \(x=-\frac{3}{5} a\) similarly
State final answer \(x>5 a, x<-\frac{3}{5} a\)
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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