How do you solve #2| - 5r - 10| = 0#?

1 Answer
Andy Y.
May 25, 2017

#r=-2#

Explanation:

Any expression of numbers or expressions multiplied by each other will equal zero if (and only if) at least one of the factors is also zero. That's because #0xx"anything"=0#.

In this case, we have

#2xx(abs(-5r-10))=0#

The two things multiplied are the #2# and the #abs(-5r-10)#. So to equal zero, either the #2# has to be #0# (which is absurd...#2# simply is not equal to #0#), or the #abs(-5r-10)=0#. Simple logic says it has to be the other one.

If the #abs("anything")=0# then the "anything" inside the absolute value must also be zero. Therefore,

#-5r-10=0#
#-5r=10#
#r=-2#

ANSWER: #r=-2# will make the whole expression true.

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