The absolute value of the sum of -5 and twice a number is 19. Find the number. I have a problem with this question because i do not fully understand absolute value and this question is a little trucky for me.
If the absolute value of the sum of -5 and twice the number is 19, then that means either:
$-5+2x=19$ or $-5+2x=-19$.
$2x=24$ or $2x=-14$.
$x=12$ or $x=-7$.
As @Dr.SonnhardGraubner wrote, the equation resulting from the words in your question is
Now you just need to solve that. Use one of these key facts, true if we know that $b\ge 0$:
$|a|=b\qquad$ is equivalent to $\qquad a=-b\quad$ or $\quad a=b$.
$|a|<b\qquad$ is equivalent to $\qquad -b<a<b$.
$|a|>b\qquad$ is equivalent to $\qquad a<-b\quad$ or $\quad b<a$.
I hope this helps you to better understand absolute value. Let us know if you cannot finish.