Solve for $G$. $D=\frac{4}{7}(F+G)$
Answer (2)
Multiply both sides of the equation by 4 7 : 4 7 D = F + G .
Subtract F from both sides: 4 7 D − F = G .
Express G in terms of D and F .
The solution is: G = 4 7 D − F .
Explanation
Understanding the Problem We are given the equation D = 7 4 ( F + G ) and our goal is to isolate G on one side of the equation. This involves using algebraic manipulations to rearrange the equation.
Multiplying by the Reciprocal First, we want to get rid of the fraction by multiplying both sides of the equation by 4 7 . This gives us: 4 7 D = 4 7 × 7 4 ( F + G ) 4 7 D = F + G
Isolating G Now, to isolate G , we subtract F from both sides of the equation: 4 7 D − F = F + G − F 4 7 D − F = G
Final Answer Therefore, we have solved for G and found that G = 4 7 D − F .
Examples
In physics, this type of equation can be used to relate forces. For example, D could represent a force that is proportional to the sum of two other forces, F and G . If you know the value of D and F , you can solve for G to find the magnitude of the unknown force. This is useful in scenarios like calculating the net force on an object or determining the components of a force.
To solve for G in the equation D = 7 4 ( F + G ) , we multiply by 4 7 to eliminate the fraction and then isolate G . The final expression is G = 4 7 D − F . This allows us to calculate G when the values of D and F are known.
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