1
$\begingroup$

I have a question about distribution and absolute values. I was solving a problem and was wondering if it would be okay to distribute a number into an absolute value with two terms. For example $3|2x+3|+3x^2-5$, is it okay to distribute the $3$ into $|2x+3|$ to get $|6x+9|$? I have searched this on Google but people said it was not okay to do it, but someone else said it was okay to do it. I am really confused, could someone clear this up for me?

$\endgroup$
3
$\begingroup$

If the multiplier is non-negative, it's OK. For example, $2|x| = |2x|$ but $-3|x|=-|3x|$.

$\endgroup$
1
$\begingroup$

There is a definite fact to use here, namely that |a*b| = |a|*|b| for any two real numbers.

So for 3|2x+3| since 3>0 we have : 3*|2x+3| = |3||(2x+3)| = |(3)(2x+3)| (using above fact) which is then |6x+9| just by multiplying out the inside.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.