Question

How many solutions will the equation 4h+6=14−12(16−8h)
have?(1 point)
Responses

infinite/many solutions
infinite/many solutions

no solution
no solution

one solution
one solution

two solutions

Answer 1

To determine how many solutions the equation \(4h + 6 = 14 - 12(16 - 8h)\) has, we can simplify and solve it step by step.

1. 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:

\[
4h + 6 = 14 - 192 + 96h
\]
\[
4h + 6 = -178 + 96h
\]

2. Now, isolate the variable \(h\). Move all terms involving \(h\) to one side and constant terms to the other:

\[
4h - 96h = -178 - 6
\]
\[
-92h = -184
\]

3. Now, solve for \(h\) by dividing both sides by \(-92\):

\[
h = \frac{-184}{-92}
\]

4. 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**.