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how do I solve 1/2(b-10)+2b=25 I need to know step by step and also need to know how to check my answer. this is for algebra

1 Answer

3 votes

\text{b = 12}

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

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