Question

If b<0 and |b|=4b+15, then what is the value of b?

Answer 1

\[\left| b \right|=4b+15\]can be written as\[b=4b +15\]or\[b=-(4b+15)\]

Answer 2

after simplifying both of the equations, you'll get a solution of \[b=-5\]and\[b=-3\]both of which satisfy the condition\[b<0\]

Answer 3

This is a MCQ. I have the option of choosing only one of the above.

Answer 4

Ok. So what you can do is try substituting both values into the original equation. So if you substitute \[b=-5\]into\[|b|=4b+15\]you'll see that \[LHS=|b|=|-5|=5\]and\[RHS=4b+15=4(-5)+15=-5\]So\[RHS \neq LHS\]But if you substitute\[b=-3\]then\[LHS=|-3|=3\]and\[RHS=4(-3)+15=3\]So\[LHS = RHS\]So your answer will be \[b=-3\]

Answer 5

Thank you so much. :)

Answer 6

You would have gotten the right answer directly.
As b<0
=> |b| =-b.