Question

Find the value of the expression |2x−8| where x=−2.5; 0; 4; 5; 9.5.

Answer 1

The absolute value $|x|$ returns the "positive version" of a number. In other words, if $x$ is already positive, then $|x|=x$. Otherwise, if $x$ is negative, then the absolute value changes its sign, so that it returns positive: $|x|=-x$.

So, in this case, we have to plug the required values for $x$ in the expression $2x-8$. Then, if the result is positive we're ok, otherwise we discard the negative sign.

We have:

$x=-2.5 \implies |2x-8| = |-5-8|=|-13|=13$

$x=0 \implies |2x-8| = |0-8|=|-8|=8$

$x=4 \implies |2x-8| = |8-8|=|0|=0$

$x=5 \implies |2x-8| = |10-8|=|2|=2$

$x=9.5 \implies |2x-8| = |19-8|=|11|=11$