Solve this formula for C. Check all answers that are true. (4 points) Responses First step is to multiply by 9 on each side. First step is to multiply by 9 on each side. First step is to add 32 to both sides. First step is to add 32 to both sides. The next step from F - 32 = 9/5 C, could be to multiply both sides by 5 The next step from F - 32 = 9/5 C, could be to multiply both sides by 5 The next step from F - 32 = 9/5 C, could be to divide both sides by 5 The next step from F - 32 = 9/5 C, could be to divide both sides by 5 Solution: 5/9F - 32 = C Solution: 5/9F - 32 = C To solve this equation for C, you would have to distribute at some point.

Question

GPT-4o mini · Answer

Let's analyze the equation $ F - 32 = \frac{9}{5} C $ and solve it for $ C $. 1. **Starting Equation**: $$ F - 32 = \frac{9}{5} C $$ 2. **First Step Options**: - **Multiplying by 9** on each side: This isn't a suitable first step since it complicates the equation unnecessarily. - **Adding 32** to both sides: This is not the first step for solving for $ C $ directly, as we should be isolating $ C $ instead. 3. **Next Steps**: - **Multiply both sides by 5**: This can be done to eliminate the fraction, but it's not necessary to get to $ C $ directly. However, it is a valid operation that could be done. - **Divide both sides by 5**: This step cannot be done as the $ \frac{9}{5}C $ doesn't allow for direct division by 5 on both sides. 4. **Steps to Solve for $ C $**: Let's proceed with solving for $ C $: $$ F - 32 = \frac{9}{5} C $$ Multiply both sides by $ \frac{5}{9} $ to isolate $ C $: $$ \frac{5}{9}(F - 32) = C $$ This simplifies to: $$ C = \frac{5}{9}(F - 32) $$ 5. **Final Rearrangement**: Distributing the $ \frac{5}{9} $: $$ C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9} $$ While distributing was not necessary for the immediate solution, it provides clarity in the final answer. Now, let's summarize which statements are true based on this reasoning: - **The first step is to multiply by 9 on each side.**: False - **The first step is to add 32 to both sides.**: False - **The next step from $ F - 32 = \frac{9}{5} C $, could be to multiply both sides by 5.**: True (as a manipulation but not a necessary step to isolate $ C $) - **The next step from $ F - 32 = \frac{9}{5} C $, could be to divide both sides by 5.**: False - **Solution: $ \frac{5}{9}F - 32 = C $**: False (the correct is $ C = \frac{5}{9}F - \frac{160}{9} $ after full distribution) - **To solve this equation for $ C $, you would have to distribute at some point.**: False (distribution is not necessary to isolate $ C $ but helps clarify) Conclusions: - True Statements: The next step from $ F - 32 = \frac{9}{5} C $ could be to multiply both sides by 5. - False Statements: All other statements.