Question

For a non-zero vector $\overrightarrow{a}$, the set of real number satisfying the inequality $\left|(5-x)a\right|<\left|2a\right|$ consists of all $x$ such that

• A. $0<x<3$
• B. $3<x<7$
• C. $-7<x<-3$
• D. $-7<x<3$

Answer 1

The correct option is B $3<x<7$

We have $\left|(5-x)a\right|<\left|2a\right|$

$\Rightarrow {\left|(5-x)a\right|}^2<{\left|2a\right|}^2$

$\Rightarrow {(5-x)}^2<4$

$\Rightarrow 5-x<2$ or $5-x>-2$

$\Rightarrow 5-2<x$ or $-x>-7$

$\Rightarrow 3<x$ or $x<7$

$\Rightarrow 3<x<7$