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
.
Remaining Attempts : 3

Answer 1

To determine how many of the given equations have the solution set \(\{5\}\), we will solve each equation and see if \(x = 5\) is the only solution.

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

\(2(x - 3) + 1 = 5\)

Subtract 1 from both sides:

\(2(x - 3) = 4\)

Divide by 2:

\(x - 3 = 2\)

Add 3 to both sides:

\(x = 5\)

So, the solution set for this equation is \(\{5\}\).

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

Multiply both sides by 15:

\(3b = 15\)

Divide by 3:

\(b = 5\)

Therefore, the solution set for this equation is also \(\{5\}\).

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

Add 30 to both sides:

\(2h = 70\)

Divide by 2:

\(h = 35\)

Therefore, the solution set for this equation is \(\{35\}\).

Now we summarize:

- The first equation gives a solution set of \(\{5\}\).
- The second equation gives a solution set of \(\{5\}\).
- The third equation gives a solution set of \(\{35\}\).

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

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