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

Answer 1

Let's go through Cupid's original steps to see where the error occurred. The original equation is:

\[
-3 + \frac{x}{4} = -7
\]

To solve for \( x \), we can follow these steps correctly:

1. **Add 3 to both sides of the equation**:

\[
-3 + \frac{x}{4} + 3 = -7 + 3
\]

This simplifies to:

\[
\frac{x}{4} = -4
\]

2. **Now, multiply both sides by 4** to eliminate the fraction:

\[
4 \cdot \frac{x}{4} = -4 \cdot 4
\]

This gives us:

\[
x = -16
\]

So, the correct solution to the equation is:

\[
\boxed{-16}
\]

Now, if we look at Cupid's work, after stating \( x/4 - 3 = -7 \), he seems to have multiplied incorrectly and added wrongly. Specifically, multiplying both sides by 4 should have given him \(\frac{x}{4} \times 4 = -7 \times 4\) leading directly to \(x = -28\) without the intermediate steps he provided, which weren't handled cleanly. Ultimately, from \( \frac{x}{4} = -4\) we get \( x = -16\).