Question

Cupid solved the equation −3 + x/4 = −7 . He seems to have made an error in his work because the solution he found does not work. Observe Cupid's work to find his error and correct it to find the solution to the equation. x/4−3= −7 x/4 (4)−3= −7(4) Using the Multiplication Property of Equality x−3+3 = −28+3 Using the Addition Property of Equality x = −25

How could Cupid have correctly started to solve the equations to avoid his error? Select all that apply. (2 points) Responses Cupid did not make any errors. His answer was correct. Cupid did not make any errors. His answer was correct. Cupid could have divided both sides by 4 instead of multiplying. Cupid could have divided both sides by 4 instead of multiplying. Cupid could have used the Addition Property before the Multiplication Property Cupid could have used the Addition Property before the Multiplication Property Cupid could have multiplied all terms by 4 first using the Multiplication Identity. Cupid could have multiplied all terms by 4 first using the Multiplication Identity. Cupid could have subtracted 3 from both sides first. Cupid could have subtracted 3 from both sides first. Cupid could move the variable from the left side to the right side first using the Subtraction Property of Equality

Answer 1

To solve Cupid's original equation \(-3 + \frac{x}{4} = -7\), he made an error in his method. The correct approach involves following the proper steps to isolate \(x\).

1. **Original Equation**: \(-3 + \frac{x}{4} = -7\)

To solve this correctly, we can first isolate the \(\frac{x}{4}\) term:

2. **Add 3 to both sides**:
\(-3 + \frac{x}{4} + 3 = -7 + 3\)
This simplifies to:
\(\frac{x}{4} = -4\)

3. **Multiply both sides by 4**:
\(\frac{x}{4} \cdot 4 = -4 \cdot 4\)
This gives:
\(x = -16\)

Now, let's analyze the options provided regarding how Cupid could have correctly started solving the equation:

1. **Cupid did not make any errors. His answer was correct.**
- **Incorrect**, his answer was \(x = -25\), which is wrong.

2. **Cupid could have divided both sides by 4 instead of multiplying.**
- **Incorrect**, dividing both sides here wouldn’t be the first logical step.

3. **Cupid could have used the Addition Property before the Multiplication Property.**
- **Correct**, subtracting 3 first to isolate \(\frac{x}{4}\) would be a logical first step.

4. **Cupid could have multiplied all terms by 4 first using the Multiplication Identity.**
- **Correct**, he could have multiplied all terms by 4 to eliminate the fraction at the beginning.

5. **Cupid could have subtracted 3 from both sides first.**
- **Correct**, this is a valid first step for isolating the variable term.

6. **Cupid could move the variable from the left side to the right side first using the Subtraction Property of Equality.**
- **Incorrect**, moving terms is not an optimal strategy in this case.

**In summary, the correct responses are:**
- Cupid could have used the Addition Property before the Multiplication Property.
- Cupid could have multiplied all terms by 4 first using the Multiplication Identity.
- Cupid could have subtracted 3 from both sides first.