Question

Kelia is solving an equation for x . Her second step is to multiply both sides of the equation by 4. Which equation is she solving?(1 point) Responses 6 + x4 = 1 6 plus Start Fraction x over 4 End Fraction equals 1 6 + 4x = 1 6 plus 4 x equals 1 4 + 6x = 1 4 plus 6 x equals 1 4 + x6 = 1

Answer 1

To find an equation that would make sense for Kelia's second step of multiplying both sides by 4, let's analyze the options provided:

1. \( 6 + \frac{x}{4} = 1 \)
2. \( 6 + 4x = 1 \)
3. \( \frac{x}{6} = 1 \)

From these, if she multiplies both sides of the equation by 4, we need to see which would yield a valid transformation.

1. **For \( 6 + \frac{x}{4} = 1 \)**:
- Multiply both sides by 4:
- \( 4(6 + \frac{x}{4}) = 4(1) \)
- This simplifies to \( 24 + x = 4 \), which is valid.

2. **For \( 6 + 4x = 1 \)**:
- Multiply both sides by 4:
- \( 4(6 + 4x) = 4(1) \)
- This simplifies to \( 24 + 16x = 4 \), which is also valid.

3. **For \( \frac{x}{6} = 1 \)**:
- Multiply both sides by 4:
- \( 4(\frac{x}{6}) = 4(1) \)
- This simplifies to \( \frac{4x}{6} = 4 \), which is also valid but not leading to a straightforward relationship connected to the other equations.

However, only the first one leads to a more meaningful transformation (getting \( x \) alone is much easier).

Given all three options, the clearest equation where multiplying by 4 has a practical sense in solving for \( x \) is:

**6 + \( \frac{x}{4} = 1 \)**

Thus, the answer is **6 + \( \frac{x}{4} = 1 \)**.