Question

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

2(x−3)+1=5


3b/15=1


2h−30=40


The number of equations that have the solution set {5}
is: __

Answer 1

To determine how many of the given equations have the solution set \(\{5\}\), we will solve each equation one by one.

**First equation:**
\[
2(x - 3) + 1 = 5
\]
Start by simplifying:
\[
2(x - 3) + 1 = 5 \implies 2(x - 3) = 5 - 1 \implies 2(x - 3) = 4
\]
Now divide by 2:
\[
x - 3 = 2 \implies x = 5
\]
This equation has the solution \(x = 5\).

**Second equation:**
\[
\frac{3b}{15} = 1
\]
Simplify the left side:
\[
\frac{b}{5} = 1
\]
Now multiply both sides by 5:
\[
b = 5
\]
This equation has the solution \(b = 5\).

**Third equation:**
\[
2h - 30 = 40
\]
Add 30 to both sides:
\[
2h = 70
\]
Now divide by 2:
\[
h = 35
\]
This equation has the solution \(h = 35\), which does not equal 5.

Now, we summarize the findings:
1. The first equation has the solution \(x = 5\).
2. The second equation has the solution \(b = 5\).
3. The third equation does not have the solution \(h = 5\).

Thus, the total number of equations that have the solution set \(\{5\}\) is:

\[
\boxed{2}
\]