Question

Find the solution and interval notation of x , in 2x < 4x - 12

Answer 1

Step-by-step explanation:

2x+12<4x

12<4x-2x

12<2x

6<x

it means that for every value of x, x is greater than 6

Answer 2

Answer:

$2x<4x-12\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>6\:\\ \:\mathrm{Interval\:Notation:}&\:\left(6,\:\infty \:\right)\end{bmatrix}$

Step-by-step explanation:

$2 x < 4 x - 1 2$

$\gray{\mathrm{ S u b t r a c t \: } 4 x \mathrm{ \: f r o m \: b o t h \: s i d e s }}$

$2 x - 4 x < 4 x - 1 2 - 4 x$

$\gray{\mathrm{ S i m p l i f y }}$

$- 2 x < - 1 2$

$\gray{\mathrm{ M u l t i p l y \: b o t h \: s i d e s \: b y \: - 1 \: \left( r e v e r s e \: t h e \: i n e q u a l i t y \right)}}$

$\left( - 2 x \right) \left( - 1 \right) > \left( - 1 2 \right) \left( - 1 \right)$

$\gray{\mathrm{ S i m p l i f y }}$

$2 x > 1 2$

$\gray{\mathrm{ D i v i d e \: b o t h \: s i d e s \: b y \: }2}$

$\dfrac{ 2 x }{ 2 } > \dfrac{ 1 2 }{ 2 }$

$\gray{\mathrm{ S i m p l i f y }}$

$x > 6$