Question

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

2(x−3)+1=5


3b15=1


2h−30=40


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

Answer 1

To determine how many of the equations have the solution set {5}, we will solve each equation for its respective variable and check if the solution is 5.

1. **Equation**: \( 2(x - 3) + 1 = 5 \)

Solving for \(x\):
\[
2(x - 3) + 1 = 5
\]
\[
2(x - 3) = 5 - 1
\]
\[
2(x - 3) = 4
\]
\[
x - 3 = 2
\]
\[
x = 5
\]
**Solution**: \(x = 5\).

2. **Equation**: \( 3b = 15 \)

Solving for \(b\):
\[
3b = 15
\]
\[
b = \frac{15}{3} = 5
\]
**Solution**: \(b = 5\).

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

Solving for \(h\):
\[
2h - 30 = 40
\]
\[
2h = 40 + 30
\]
\[
2h = 70
\]
\[
h = \frac{70}{2} = 35
\]
**Solution**: \(h = 35\) (not 5).

Now, let's summarize the solutions:
1. From the first equation, the solution is 5.
2. From the second equation, the solution is 5.
3. From the third equation, the solution is 35.

Thus, the number of equations that have the solution set {5} is **2**.

The answer is:
The number of equations that have the solution set {5} is **2**.