Question

How many of the following equations have the solution set {8}?

(2 points)
Responses

−6(1+4x) = −198
−6(1+4x) = −198

b−44 = 1
b−44 = 1

−4 + n8 = −5
−4 + n8 = −5

−8(−7+r) = 120
−8(−7+r) = 120

−9p = −72

Answer 1

Let's solve each of the given equations to check if the solution set is \(\{8\}\).

1. **Equation:** \(-6(1 + 4x) = -198\)

Rearranging gives:
\[
1 + 4x = \frac{-198}{-6}
\]
\[
1 + 4x = 33 \quad \Rightarrow \quad 4x = 33 - 1
\]
\[
4x = 32 \quad \Rightarrow \quad x = \frac{32}{4} = 8
\]

**Solution Set:** \(\{8\}\)

2. **Equation:** \(b - 44 = 1\)

Rearranging gives:
\[
b = 1 + 44
\]
\[
b = 45
\]

**Solution Set:** \(\{45\}\)

3. **Equation:** \(-4 + n8 = -5\)

Rearranging gives:
\[
n8 = -5 + 4
\]
\[
n8 = -1 \quad \Rightarrow \quad n = \frac{-1}{8}
\]

**Solution Set:** \(\left\{\frac{-1}{8}\right\}\)

4. **Equation:** \(-8(-7 + r) = 120\)

Rearranging gives:
\[
-7 + r = \frac{120}{-8}
\]
\[
-7 + r = -15 \quad \Rightarrow \quad r = -15 + 7
\]
\[
r = -8
\]

**Solution Set:** \(\{-8\}\)

5. **Equation:** \(-9p = -72\)

Rearranging gives:
\[
p = \frac{-72}{-9}
\]
\[
p = 8
\]

**Solution Set:** \(\{8\}\)

Now, we summarize our findings:

- **Equation 1:** \(\{8\}\)
- **Equation 2:** \(\{45\}\)
- **Equation 3:** \(\left\{\frac{-1}{8}\right\}\)
- **Equation 4:** \(\{-8\}\)
- **Equation 5:** \(\{8\}\)

**Count of equations with the solution set \(\{8\}\):**
- The first equation and the fifth equation both have \(\{8\}\) as their solution set.

Thus, the total number of equations that have the solution set \(\{8\}\) is **2**.