Solve for $b$.
$r=(b-6) m$
Answer (2)
Divide both sides of the equation by m : m r = b − 6 .
Add 6 to both sides of the equation: b = m r + 6 .
The solution for b is: b = m r + 6 .
Explanation
Understanding the Problem We are given the equation r = ( b − 6 ) m and our goal is to isolate b on one side of the equation.
Dividing by m To isolate b , we first need to get rid of the m that is multiplying the term ( b − 6 ) . We can do this by dividing both sides of the equation by m . This gives us: m r = m ( b − 6 ) m m r = b − 6
Adding 6 Now, we need to get rid of the − 6 that is being subtracted from b . We can do this by adding 6 to both sides of the equation: m r + 6 = b − 6 + 6 m r + 6 = b
Final Answer Therefore, we have solved for b : b = m r + 6
Examples
Imagine you are calculating the final grade in a class. The final grade r depends on the number of bonus points b you earned above a base of 6, multiplied by the weight of the bonus points m . If you know your final grade r and the weight m , you can solve for b to find out how many bonus points you earned. This algebraic manipulation helps in understanding relationships between variables and solving for unknowns in various real-life scenarios.
To solve for b in the equation r = ( b − 6 ) m , first divide both sides by m to get m r = b − 6 . Then, add 6 to both sides to isolate b , resulting in b = m r + 6 .
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