To determine which equation Kelia is solving, we need to identify an equation that would require multiplying both sides by 4 as a logical second step in solving for \( x \).
Let's analyze the given options:
-
\( 4 + \frac{x}{6} = 1 \)
- If we multiply both sides by 4, the left side becomes \( 4 \cdot (4 + \frac{x}{6}) \) which does not simplify nicely to isolate \( x \) easily.
-
\( 6 + \frac{x}{4} = 1 \)
- Multiplying by 4 here would give \( 4 \cdot (6 + \frac{x}{4}) \), which also complicates isolating \( x \).
-
\( 4 + 6x = 1 \)
- Multiplying by 4 yields \( 4(4 + 6x) = 16 + 24x \), which again complicates isolating \( x \).
-
\( 6 + 4x = 1 \)
- If we multiply both sides by 4, we get \( 4(6 + 4x) = 24 + 16x \), simplifying the expression on both sides but still not directly isolating \( x \).
Based on these observations, all options somewhat lead to manipulating equations without a straightforward path. However, multiplying equations involving fractions or expressions containing \( x \) generally signals an attempt to eliminate that fraction or isolate \( x \).
Among the choices, \( 4 + \frac{x}{6} = 1 \) stands out as an equation where multiplying through by 4 simplifies the fraction resulting:
\[ 4 \left(4 + \frac{x}{6}\right) = 4 \cdot 1 \]
\[ 16 + \frac{4x}{6} = 4 \]
Thus, it appears that the first equation \( 4 + \frac{x}{6} = 1 \) is the best candidate for an equation where multiplying by 4 is a relevant and useful step in solving it for \( x \).
So, the correct response is:
4 + Start Fraction x over 6 End Fraction = 1.
1 answer