Question

How many of the following equations have the solution set {5}
?

2(x−3)+1=5

3b/15 = 1

2h − 30 = 40

(1 point)
The number of equations that have the solution set {5}
is

Answer 1

Let's solve each equation to see if they have the solution \(5\).

1. **Equation:** \( 2(x−3)+1=5 \)

Substitute \(x = 5\):
\[
2(5 - 3) + 1 = 2(2) + 1 = 4 + 1 = 5
\]
This equation is satisfied when \(x = 5\).

2. **Equation:** \( \frac{3b}{15} = 1 \)

Multiply both sides by 15:
\[
3b = 15
\]
Divide by 3:
\[
b = 5
\]
This equation is also satisfied when \(b = 5\).

3. **Equation:** \( 2h - 30 = 40 \)

Add 30 to both sides:
\[
2h = 70
\]
Divide by 2:
\[
h = 35
\]
This equation is not satisfied when \(h = 5\).

Now, let's summarize the results:
- The first equation has the solution \(5\).
- The second equation has the solution \(5\).
- The third equation does not have the solution \(5\).

The number of equations that have the solution set \(\{5\}\) is **2**.