Problem

(b) Make $c$ the subject of $g=\frac{c+3}{4+c}-7$

Answer

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Answer

\(\boxed{c = \frac{4g - 25}{g + 6}}\)

Steps

Step 1 ：Add 7 to both sides: \(g + 7 = \frac{c + 3}{4 + c}\)

Step 2 ：Multiply both sides by \((4 + c)\): \((g + 7)(4 + c) = c + 3\)

Step 3 ：Expand and simplify: \(4g + gc + 28 + 7c = c + 3\)

Step 4 ：Rearrange to solve for c: \(gc + 6c - 4g = -25\)

Step 5 ：Factor out c: \(c(g + 6) = 4g - 25\)

Step 6 ：Divide by \((g + 6)\): \(c = \frac{4g - 25}{g + 6}\)

Step 7 ：\(\boxed{c = \frac{4g - 25}{g + 6}}\)

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