To determine how many solutions the equation \(4h + 6 = 14 - 12(16 - 8h)\) has, we can simplify and solve it step by step.
- Start by distributing on the right side:
\[ 4h + 6 = 14 - 12 \cdot 16 + 12 \cdot 8h \]
Calculating \(12 \cdot 16\):
\[ 12 \cdot 16 = 192 \]
So the equation becomes:
\[ 4h + 6 = 14 - 192 + 96h \] \[ 4h + 6 = -178 + 96h \]
- Now, isolate the variable \(h\). Move all terms involving \(h\) to one side and constant terms to the other:
\[ 4h - 96h = -178 - 6 \] \[ -92h = -184 \]
- Now, solve for \(h\) by dividing both sides by \(-92\):
\[ h = \frac{-184}{-92} \]
- Simplifying the fraction:
\[ h = 2 \]
Since we solved for \(h\) and found a unique value, the equation has one solution.
Thus, the answer is one solution.
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