Question

-10-|1+4b|=-19
Y = 0

Answer 1

b=2 or b=-2.5

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.

`-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\(-|1+4b|)/(-1) =(-9)/(-1) \\|1+4b|=9`

We now have the absolute value isolated. We will set it equal to both 9 and -9.

`1+4b=9\\1-1+4b=9-1\\4b=8\\b=2`

and

`1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=(-10)/(4)=(-5)/(2)=  -2.5`