Answer:
b=2 or b=-2.5
Step-by-step explanation:
We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.
[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]
We now have the absolute value isolated. We will set it equal to both 9 and -9.
[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]
and
[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}= -2.5[/tex]
