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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.

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    $\begingroup$ Step 1: write it as an equation with symbols. You might follow tradition and call your unknown number $x$. $\endgroup$ – davidlowryduda Aug 15 '15 at 19:32
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    $\begingroup$ i would say $|-5+2x|=19$ $\endgroup$ – Dr. Sonnhard Graubner Aug 15 '15 at 19:32
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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 $x=-7$.

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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.

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