Worked example: absolute value equations with one solution

Get rid of the absolute value notation by setting up the two equations so that in the first equation, the quantity inside absolute notation is positive. In the second equation, it is negative. You will

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Remove the absolute value bars by setting up a compound inequality . When can you drop absolute value? So, summarizing we can see that if b is zero then we can just drop the

What we need is to eliminate first the negative sign of the absolute value symbol before we can proceed. Observe that the given equation has a coefficient of