Question

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

two solutions
two solutions - no response given

one solution
one solution - incorrect

infinite/many solutions
infinite/many solutions - no response given

no solution

Answer 1

wrong

Answer 2

To solve the equation \( 4h + 6 = 14 - 12(16 - 8h) \), we first expand and simplify both sides.

1. Start with the right side:
\[
12(16 - 8h) = 192 - 96h
\]
Thus, we rewrite the equation:
\[
4h + 6 = 14 - (192 - 96h)
\]
Simplifying,
\[
4h + 6 = 14 - 192 + 96h
\]
Combining like terms gives:
\[
4h + 6 = 96h - 178
\]

2. Now, let's get all the terms involving \(h\) on one side:
\[
4h - 96h = -178 - 6
\]
This simplifies to:
\[
-92h = -184
\]

3. Divide both sides by -92:
\[
h = \frac{-184}{-92} = \frac{184}{92} = 2
\]

The equation simplifies to just one solution: \( h = 2 \).

Therefore, the answer is **one solution**.

Answer 3

Let's carefully go through the solution step-by-step again to find the correct answer for the equation \( 4h + 6 = 14 - 12(16 - 8h) \).

1. **Start with the original equation:**
\[
4h + 6 = 14 - 12(16 - 8h)
\]

2. **Distribute the \(-12\) on the right side:**
\[
-12(16 - 8h) = -192 + 96h
\]
So the equation now is:
\[
4h + 6 = 14 - 192 + 96h
\]
This simplifies to:
\[
4h + 6 = -178 + 96h
\]

3. **Rearrange the equation to isolate variables on one side:**
\[
4h - 96h = -178 - 6
\]
Combining like terms gives us:
\[
-92h = -184
\]

4. **Solve for \(h\):**
\[
h = -184 / -92 = 2
\]

Thus, we have determined that the equation has **one solution** \( h = 2 \).

If the answer was marked incorrect previously, please check if the original equation provided had a different form or if there were any additional constraints. However, based on the equation you've presented, the correct answer is indeed **one solution**.