Question

The Celsius to Fahrenheit formula: F = 9 over 5C + 32
Solve this formula for C. Check ALL!!! Answers that are TRUE!!..

options:

A). First step is to multiply by 9 on each side.

B). First step is to add 32 to both sides.

C). The next step from F - 32 = 9/5 C, could be to multiply both sides by 5

D). The next step from F - 32 = 9/5 C, could be to divide both sides by 5

E). Solution: 5/9F - 32 = C

F). To solve this equation for C, you would have to distribute at some point.

Answer 1

Izzie is trying to solve this inequality: 3(t + 1) − 4t ≥ −5

After she solves it, she shows it to you and asks you if she did it correctly.

This is the work she completed:

Step 1: 3t + 3 − 4t ≥ −5

Step 2: −t + 3 ≥ −5

Step 3: −t ≥ −2

Step 4: t ≤ 2

options:

1. Izzie made no mistakes in solving this inequality. True or false?

2. The correct answer should have been t≤8. True or false?

3. Izzie made a mistake going from step 3 to step 4. True or false?

4. Izzie made a mistake going from step 1 to step 2. True or false?


5. Izzie should not have changed the inequality symbol from ≥ to ≤
True or false?

6. Izzie made a mistake going from step 2 to step 3 True or false?

Answer 2

To solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \), let's go through it step by step and evaluate the options provided.

1. Start with the original equation:
\[
F = \frac{9}{5}C + 32
\]

2. Subtract 32 from both sides:
\[
F - 32 = \frac{9}{5}C
\]

3. To isolate \( C \), you can multiply both sides by \( \frac{5}{9} \):
\[
C = \frac{5}{9}(F - 32)
\]

Now let's check each option.

A). **First step is to multiply by 9 on each side.**
- FALSE. The first step to isolate C is to subtract 32 from both sides, not multiply by 9.

B). **First step is to add 32 to both sides.**
- FALSE. The first step is to subtract 32 from both sides, not add.

C). **The next step from F - 32 = 9/5 C, could be to multiply both sides by 5.**
- TRUE. You could multiply both sides by 5, but you need to divide by 9 afterwards to isolate C, this step is valid.

D). **The next step from F - 32 = 9/5 C, could be to divide both sides by 5.**
- FALSE. Dividing both sides by 5 would not isolate C, you need to multiply first.

E). **Solution: 5/9F - 32 = C**
- FALSE. The correct solution is \( C = \frac{5}{9}(F - 32) \) or equivalently \( C = \frac{5}{9}F - \frac{160}{9} \) after distributing.

F). **To solve this equation for C, you would have to distribute at some point.**
- TRUE. You would distribute when rearranging to get to the final solution.

**Summary:**
- Options C and F are TRUE.
- Options A, B, D, and E are FALSE.

Answer 3

Let's carefully go through Izzie's work on the inequality and evaluate her solution step by step.

Starting with the inequality:
\[
3(t + 1) - 4t \geq -5
\]

**Step-by-step work**

1. Distributing \(3\) in the first term:
\[
3t + 3 - 4t \geq -5
\]
This is correct as shown in Step 1.

2. Combining like terms:
\[
(3t - 4t) + 3 \geq -5 \implies -t + 3 \geq -5
\]
This is also correct as shown in Step 2.

3. Now, subtract \(3\) from both sides:
\[
-t \geq -5 - 3 \implies -t \geq -8
\]
So, at this point, we have:
\[
-t \geq -8
\]

4. Now, to isolate \(t\), we multiply both sides by \(-1\) and remember to flip the inequality:
\[
t \leq 8
\]

So the correct solution to the inequality is:
\[
t \leq 8
\]

Now, let's check Izzie's steps against the correct solution:

1. **Izzie made no mistakes in solving this inequality.**
- **False.** She concluded with \(t \leq 2\), but the correct answer is \(t \leq 8\).

2. **The correct answer should have been \(t \leq 8\).**
- **True.** As derived above.

3. **Izzie made a mistake going from step 3 to step 4.**
- **True.** She incorrectly concluded with \(t \leq 2\) instead of the correct conclusion \(t \leq 8\).

4. **Izzie made a mistake going from step 1 to step 2.**
- **False.** Her work from step 1 to step 2 was correct.

5. **Izzie should not have changed the inequality symbol from ≥ to ≤.**
- **True.** Because when multiplying/dividing by a negative number (in step 3), the inequality direction must flip.

6. **Izzie made a mistake going from step 2 to step 3.**
- **False.** The transition from step 2 to step 3 was correct; she just miscalculated the next step.

**Summary of answers:**
1. False
2. True
3. True
4. False
5. True
6. False