Question

Solve the following equations:
Find the least integral value of $x$ which satisfies the equation $|x-3|+2|x+1|=4.$

Answer 1

The given equation is

$|x-3|+2|x+1|=4$

$\therefore$ We have three cases

$i.)x<-1,ii.)-1<x<3,iii.)x>3$

Hence the respective equations in three cases are

$i.\left)\right(3-x)+2(-x-1)=4,ii.)(3-x)+2(x+1)=4,iii.\left)\right(x-3)+2(x+1)=4$

in first case the equation becomes

$i.)-3x=3$ implies $x=-1$

in second case the equation becomes

$ii.)5+x=4$ implies $x=-1$ but we assumed $x>-1$ therefore no solution in this case$

in third case the equation becomes

$3x=5$ implies $x=5/3$ but we assumed $x>3$ therefore no solution in this case

therefore the least integral value of x is -1