Absolute value of numbers

Question

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.

Answer 1

If the absolute value of the sum of -5 and twice the number is 19, then that means either:

$-5+2x=19$ or $-5+2x=-19$.

Thus:

$2x=24$ or $2x=-14$.

Therefore:

$x=12$ or $x=-7$.

Answer 2

As @Dr.SonnhardGraubner wrote, the equation resulting from the words in your question is

$$|-5+2x|=19$$

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.