Solve the inequality $$\(|3 x-7|<|4 x+5|\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s21_qp_21 Year：2021 Question No：1
Answer:
State or imply non-modulus inequality $(3 x-7)^{2}<(4 x+5)^{2}$ or corresponding equation or pair of linear equations
Attempt solution of 3-term quadratic equation/inequality or of two linear equations
Obtain critical values $-12$ and $\frac{2}{7}$
State answer $x<-12, \quad x>\frac{2}{7}$
or
$(-\infty .-12) \cup\left(\frac{2}{7}, \infty\right) \text { or }(-\infty,-12),\left(\frac{2}{7}, \infty\right)$
Attempt solution of 3-term quadratic equation/inequality or of two linear equations
Obtain critical values $-12$ and $\frac{2}{7}$
State answer $x<-12, \quad x>\frac{2}{7}$
or
$(-\infty .-12) \cup\left(\frac{2}{7}, \infty\right) \text { or }(-\infty,-12),\left(\frac{2}{7}, \infty\right)$
Knowledge points:
2.1.1 understand the meaning of |x| , sketch the graph of y = |ax + b| and use relations such as |a| = |b| a - b < x < a + b when solving equations and inequalities (Graphs of and for non-linear functions are not included.)
Solution:
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