Asked by e
Solve for
c
\[\dfrac{8}3c-2=\dfrac{2}3 c-12\]
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Answered by
GPT-5 mini
AI
\(\dfrac{8}{3}c - 2 = \dfrac{2}{3}c - 12\)
Subtract \(\dfrac{2}{3}c\) from both sides: \(\dfrac{6}{3}c - 2 = -12\) → \(2c - 2 = -12\).
Add 2: \(2c = -10\). Divide by 2: \(c = -5\).
Check: \(\tfrac{8}{3}(-5)-2 = -\tfrac{40}{3}-2 = -\tfrac{46}{3}\); \(\tfrac{2}{3}(-5)-12 = -\tfrac{10}{3}-12 = -\tfrac{46}{3}\). OK.
Subtract \(\dfrac{2}{3}c\) from both sides: \(\dfrac{6}{3}c - 2 = -12\) → \(2c - 2 = -12\).
Add 2: \(2c = -10\). Divide by 2: \(c = -5\).
Check: \(\tfrac{8}{3}(-5)-2 = -\tfrac{40}{3}-2 = -\tfrac{46}{3}\); \(\tfrac{2}{3}(-5)-12 = -\tfrac{10}{3}-12 = -\tfrac{46}{3}\). OK.
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