Believe it or not, there are many good reasons to develop your ability to rearrange equations that are important to the your field. It can save time, help you with units and save some brain space! Here are some reasons to develop your equation manipulation skills (in no particular order):
Be aware of the order of operations! Which operation can you perform first?
Rearrange the following formula for the variable \( m_2 \)
\[ \frac{K_1}{K_2} = \frac{m_1 + m_2}{m_1} \]
Solution:
Since the goal is to isolate for \( m_2 \), we want to move the variable \( m_1 \).
We need to first move the \( m_1 \) at the bottom of the fraction by multiplying both sides by \( m_1 \)
\[ \frac{K_1}{K_2} \times m_1 = \frac{m_1 + m_2}{\cancel{m_1}} \times \cancel{m_1} \]
This will move \( m_1 \) from the bottom of the right fraction to the other side of the equation
\[ \frac{K_1}{K_2} \times m_1 = m_1 + m_2 \]
Now move we move the remaining \( m_1 \) on the right side by subracting both sides by \( m_1 \)
\[ \frac{K_1m_1}{K_2} - m_1 = \cancel{m_1} + m_2 - \cancel{m_1} \]
\[ \frac{K_1m_1}{K_2} - m_1 = m_2 \]
Rearrange the following equation for \(k\),
\[ \frac{4k^3}{m} - 3 = 10 + \frac{d}{2} \]
Watch the video for the solution.