To make the expression \(54x + 6\) equivalent to \(12x + 6\), we need to determine what we need to add.
Starting from \(54x + 6\) and aiming for \(12x + 6\), we can set up the equation:
\[ 54x + 6 + \text{(??)} = 12x + 6 \]
Subtract \(6\) from both sides:
\[ 54x + \text{(??)} = 12x \]
Now, isolate \(\text{(??)}\):
\[ \text{(??)} = 12x - 54x \] \[ \text{(??)} = -42x \]
Now, we need to determine which of the given options is equivalent to \(-42x\).
Below are the responses you provided:
- \(-\frac{3}{4}x\)
- \(-x\)
- \(\frac{3}{4}x\)
- \(-2x\)
None of the provided options yield \(-42x\). It seems there is either an error in the provided options or in how the problem was presented. None of the options allow \(54x + 6 + \text{(??)}\) to equal \(12x + 6\) without introducing a different operation or modification.
If we directly analyze the required operation, one correct way to solve it could also be to subtract \(42x\) from \(54x\).
Thus, based on the context and the provided options, it might be necessary to recheck the original expression or adjust the provided responses due to a potential mismatch in expected results, as the existing options do not yield a solution that achieves equivalence with \(12x + 6\).
1 answer