Answer:
The number could be [tex]x=-6[/tex] or [tex]x=-1/3[/tex]
Step-by-step explanation:
Let
x-----> the number
Remember that
The reciprocal of a number is 1 divided by the number
we know that
[tex]x+2(\frac{1}{x})=-\frac{19}{3}[/tex]
Solve for x
Multiply by 3x both sides
[tex]3x^{2} +6=-19x\\ \\ 3x^{2}+19x+6=0[/tex]
Solve the quadratic equation by graphing
The solutions are [tex]x=-6, x=-1/3[/tex]
see the attached figure
Verify both solutions
For [tex]x=-6[/tex]
[tex]-6+2(-\frac{1}{6})=-\frac{19}{3}[/tex]
[tex]-\frac{19}{3}=-\frac{19}{3}[/tex] ----> is true
For [tex]x=-1/3[/tex]
[tex]-(1/3)+2(\frac{1}{(-1/3)})=-\frac{19}{3}[/tex]
[tex]-\frac{19}{3}=-\frac{19}{3}[/tex] ----> is true
