Question

What is the answer to 5+5|2b+2|=25

Answer 1

The absolute value is defined as two cases, if we substitute what we have in this example

`\begin{gathered} |2b+2|\text{ = }2b+2\text{ if 2b+2}\ge0, \\ |2b+2|=-(2b+2)\text{ if 2b+2<0.} \end{gathered}`

Then, if we substitute this equations

`\begin{gathered} 5+5(2b+2)\text{ = 25, and 2b+2}\ge0 \\ 5+5(-(2b+2))\text{ = 25, 2b<0.} \end{gathered}`

The first part becomes in

`\begin{gathered} 5+10b+10=25,\text{ and 2b}\ge-2, \\ 10b=10,\text{ and b}\ge-1, \\ b=1,\text{ and b}\ge-1. \end{gathered}`

Then, one solution is b=1 since both conditions are fulfilled.

From the second part we have

`\begin{gathered} 5+5(-2b-2)=25,\text{ and 2b+2<0} \\ 5-10b-10=25,\text{ and 2b<-2} \\ -10b=30,\text{ and b<}-1 \\ b=-3,\text{ and b<-1} \end{gathered}`

Thus, the other soultion is b=-3 since it satisfies both conditions.