To determine which equation Kelia is solving, we need to analyze what happens when she multiplies both sides by 4.
-
For the equation \(4 + 6x = 1\): \[ \text{Multiply both sides by 4: } 4(4 + 6x) = 4 \cdot 1 \] This results in \(16 + 24x = 4\).
-
For the equation \(6 + \frac{x}{4} = 1\): \[ \text{Multiply both sides by 4: } 4(6 + \frac{x}{4}) = 4 \cdot 1 \] This results in \(24 + x = 4\).
-
For the equation \(6 + 4x = 1\): \[ \text{Multiply both sides by 4: } 4(6 + 4x) = 4 \cdot 1 \] This results in \(24 + 16x = 4\).
-
For the equation \(4 + \frac{z}{6} = 1\): \[ \text{Multiply both sides by 4: } 4(4 + \frac{z}{6}) = 4 \cdot 1 \] This results in \(16 + \frac{4z}{6} = 4\).
Among the four equations, only the second one, \(6 + \frac{x}{4} = 1\), results in an equation that clearly and simply leads to \(x\) being isolated with a straightforward multiplication. Therefore, it's quite common to multiply fractions by a number when working toward isolating a variable.
Thus, the equation that Kelia is solving, where her second step is to multiply both sides by 4, is:
Answer: \(6 + \frac{x}{4} = 1\).