[tex]\text{b = 12}[/tex]
Explanation:[tex]1/2\mleft(b-10\mright)+2b=25[/tex][tex]\begin{gathered} \text{Expanding the parenthesis:} \\ \frac{1}{2}(b)-\text{ }\frac{1}{2}(10)\text{ + 2b = 25} \\ \frac{b}{2}\text{ - }\frac{\text{10}}{2}\text{+ 2b = 25} \end{gathered}[/tex][tex]\begin{gathered} \frac{b}{2}-5+\text{ 2b = 25} \\ \text{add 5 to both sides:} \\ \frac{b}{2}-5+5+\text{ 2b = 25 + 5} \\ \frac{b}{2}\text{ + 2b = 30} \end{gathered}[/tex][tex]\begin{gathered} \text{LCM = 2} \\ \frac{b+2(2b)}{2}\text{ = 30} \\ \frac{b\text{ + 4b}}{2}\text{ = 30} \\ mu\text{ltiply both sides by 2:} \\ 2(\frac{b\text{ + 4b}}{2})\text{ = 2(30)} \end{gathered}[/tex][tex]\begin{gathered} b\text{ + 4b = 60} \\ 5b\text{ = 60} \\ \\ \text{Divide both sides by 5:} \\ \frac{5b}{5}=\text{ }\frac{60}{5} \\ b\text{ = 12} \end{gathered}[/tex]
