Given:
The equation is:
[tex]3-2|0.5x+1.5|=2[/tex]
One solution of this equation is -2.
To find:
The another solution of the given equation.
Solution:
We have,
[tex]3-2|0.5x+1.5|=2[/tex]
It can be written as:
[tex]-2|0.5x+1.5|=2-3[/tex]
[tex]-2|0.5x+1.5|=-1[/tex]
Divide both sides by -2.
[tex]|0.5x+1.5|=0.5[/tex]
After removing the modulus, we get
[tex]0.5x+1.5=\pm 0.5[/tex]
Case I:
[tex]0.5x+1.5=0.5[/tex]
[tex]0.5x=0.5-1.5[/tex]
[tex]0.5x=-1[/tex]
Divide both sides by 0.5.
[tex]x=-2[/tex]
Case II:
[tex]0.5x+1.5=-0.5[/tex]
[tex]0.5x=-0.5-1.5[/tex]
[tex]0.5x=-2[/tex]
Divide both sides by 0.5.
[tex]x=-4[/tex]
One solution of the given equation is [tex]x=-2[/tex] and the another one is [tex]x=-4[/tex].
Therefore, the correct option is B.
