Question: Solve for $ c $: $ 7c + 4 = 3(2c + 1) + 5 $, where $ c $ represents the ratio of carbon isotopes in a microfossil sample.

Tue, 05 May 2026 23:30:54 +0000

**Solve for $ c $: $ 7c + 4 = 3(2c + 1) + 5 $, where $ c $ represents the ratio of carbon isotopes in a microfossil sample.** Understanding carbon isotope ratios helps scientists trace ancient environmental conditions—and solving the equation behind that process reveals how data modeling meets geology. When researchers analyze microfossils, they often encounter equations like $ 7c + 4 = 3(2c + 1) + 5 $, where $ c $ stands for the carbon isotope ratio used to decode climate patterns from millennia ago. Decoding this equation offers insight into both analytical chemistry and the subtle shifts in Earth’s carbon cycle. This equation isn’t just mathematical—it grounds our interpretation of past climate change. Recent interest in paleoclimate modeling has surged, driven by growing awareness of environmental trends, international climate research collaboration, and expanding public curiosity about Earth’s deep-time history. Solving for $ c $ enables scientists to turn raw isotope data into meaningful timelines of carbon exchange, helping predict future ecological responses. The equation simplifies to a straightforward algebraic solution. Expanding the right side:
$ 3(2c + 1) + 5 = 6c + 3 + 5 = 6c + 8 $
So the equation becomes:
$ 7c + 4 = 6c + 8 $
Subtracting $ 6c $ from both sides gives:
$ c + 4 = 8 $, then $ c = 4 $