Question

if | x+2. 3
x+5. 4|= 3, find the value of x​

Answer 1

Answer:

$\quad x=-\dfrac{28}{11}\quad\mathrm{or}\quad\:x=-\dfrac{8}{11}\quad\left(\mathrm{Decimal}:\quad x=-2.54545\dots,\:x=-0.72727\dots\right)$

Step-by-step explanation:

$\left|x+2.3x+5.4\right|=3$

$\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a$

$x+2.3x+5.4=-3\quad \mathrm{or}\quad \:x+2.3x+5.4=3$

$x+2.3x+5.4=-3$

$\mathrm{Add\:similar\:elements:}\:x+2.3x=3.3x$

$3.3x+5.4=-3$

$\mathrm{Multiply\:both\:sides\:by\:}10$

$3.3x\cdot \:10+5.4\cdot \:10=-3\cdot \:10$

$\mathrm{Refine}$

$33x+54=-30$

$\mathrm{Subtract\:}54\mathrm{\:from\:both\:sides}$

$33x+54-54=-30-54$

Simplify

$33x=-84$

$\mathrm{Divide\:both\:sides\:by\:}33$

$\dfrac{33x}{33}=\dfrac{-84}{33}$

$\mathrm{Simplify}$

$x=-\dfrac{28}{11}$

$x+2.3x+5.4=3$

$\mathrm{Add\:similar\:elements:}\:x+2.3x=3.3x$

$3.3x+5.4=3$

$\mathrm{Multiply\:both\:sides\:by\:}10$

$3.3x\cdot \:10+5.4\cdot \:10=3\cdot \:10$

$\mathrm{Refine}$

$33x+54=30$

$\mathrm{Subtract\:}54\mathrm{\:from\:both\:sides}$

$33x+54-54=30-54$

Simplify

$33x=-24$

$\mathrm{Divide\:both\:sides\:by\:}33$

$\dfrac{33x}{33}=\dfrac{-24}{33}$

$\mathrm{Simplify}$

$x=-\dfrac{8}{11}$

$\mathrm{Combine\:Solutions:}$

$x=-\dfrac{28}{11}\quad \mathrm{or}\quad \:x=-\dfrac{8}{11}$