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 determine which equation matches the solution set of \(\{5\}\), we will solve each equation for \(x\) and see if \(x = 5\) is the solution.

**a)** \(x + x - 9 = 1 + x\)

Combine like terms:
\[
2x - 9 = 1 + x
\]
Subtract \(x\) from both sides:
\[
2x - x - 9 = 1
\]
\[
x - 9 = 1
\]
Add 9 to both sides:
\[
x = 10
\]

**b)** \(\frac{3x}{5} + 4 = 7\)

Subtract 4 from both sides:
\[
\frac{3x}{5} = 3
\]
Multiply both sides by 5:
\[
3x = 15
\]
Divide both sides by 3:
\[
x = 5
\]

**c)** \(x^2 + 10 = 15\)

Subtract 10 from both sides:
\[
x^2 = 5
\]
Taking the square root of both sides gives:
\[
x = \sqrt{5} \text{ or } x = -\sqrt{5}
\]
(Neither solution is 5.)

**d)** \(2x - 20 = 30\)

Add 20 to both sides:
\[
2x = 50
\]
Divide both sides by 2:
\[
x = 25
\]

From the solutions, we find that:
- a) \(x = 10\)
- b) \(x = 5\) (which matches)
- c) \(x = \sqrt{5}\) or \(x = -\sqrt{5}\)
- d) \(x = 25\)

Therefore, the equation that matches the solution set of \(\{5\}\) is \(b) \frac{3x}{5} + 4 = 7\).