Question

Which equation matches the solution set of {5}?

A: x+x-9=1+x

B: 3x/5 + 4 = 7

C: x^2 + 10 = 15

D: 2x -20 =30

Answer 1

To find out which equation matches the solution set of \(\{5\}\), we need to solve each equation to see if \(x = 5\) is a solution.

**A: \(x + x - 9 = 1 + x\)**
Combine like terms:
\(2x - 9 = 1 + x\)
Subtract \(x\) from both sides:
\(2x - x - 9 = 1\)
This simplifies to:
\(x - 9 = 1\)
Add 9 to both sides:
\(x = 10\)
So, this equation does not match.

**B: \(\frac{3x}{5} + 4 = 7\)**
First, subtract 4 from both sides:
\(\frac{3x}{5} = 3\)
Now multiply both sides by 5:
\(3x = 15\)
Divide by 3:
\(x = 5\)
This equation matches.

**C: \(x^2 + 10 = 15\)**
Subtract 10 from both sides:
\(x^2 = 5\)
Take the square root of both sides:
\(x = \sqrt{5} \; \text{or} \; x = -\sqrt{5}\)
This does not match.

**D: \(2x - 20 = 30\)**
Add 20 to both sides:
\(2x = 50\)
Divide by 2:
\(x = 25\)
This does not match.

The only equation that matches the solution set of \(\{5\}\) is **B: \(\frac{3x}{5} + 4 = 7\)**.