Question

Solve the following inequation:
$|x+\frac{1}{4}|>\frac{7}{4},xϵR$
[4 MARKS]

Answer 1

Steps: 2 Marks
Calculation: 1 Mark
Answer: 1 Mark

$|x+\frac{1}{4}|>\frac{7}{4}.xϵR\Rightarrow x+\frac{1}{4}>\frac{7}{4}\Rightarrow -(x+\frac{1}{4})>\frac{7}{4}\Rightarrow x>\frac{7}{4}-\frac{1}{4}\Rightarrow x+\frac{1}{4}<-\frac{7}{4}\Rightarrow x>\frac{6}{4}\Rightarrow x<-\frac{7}{4}-\frac{1}{4}\Rightarrow x>\frac{3}{2}\Rightarrow x<-2\Rightarrow x<-2orx>\frac{3}{2}$