Question

Which equation has a solution of
x
=
2
?(1 point)
Responses

2
+
1
x
−
3
=
2
x
−
3
2 plus Start Fraction 1 over x minus 3 End Fraction equals Start Fraction 2 over x minus 3 End Fraction

1
+
2
x
−
3
=
2
x
−
3
1 plus Start Fraction 2 over x minus 3 End Fraction equals Start Fraction 2 over x minus 3 End Fraction

1
+
3
x
−
3
=
2
x
−
3
1 plus Start Fraction 3 over x minus 3 End Fraction equals Start Fraction 2 over x minus 3 End Fraction

1
+
1
x
−
3
=
2
x
−
3

Answer 1

To determine which equation has a solution of \( x = 2 \), we can substitute \( x = 2 \) into each option and check if both sides of the equation are equal.

Let's evaluate each equation:

1. **Equation:**
\( 2 + \frac{1}{x - 3} = \frac{2}{x - 3} \)
Substitute \( x = 2 \):
\( 2 + \frac{1}{2 - 3} = \frac{2}{2 - 3} \)
\( 2 + \frac{1}{-1} = \frac{2}{-1} \)
\( 2 - 1 = -2 \)
\( 1 \neq -2 \) (Not a solution)

2. **Equation:**
\( 1 + \frac{2}{x - 3} = \frac{2}{x - 3} \)
Substitute \( x = 2 \):
\( 1 + \frac{2}{2 - 3} = \frac{2}{2 - 3} \)
\( 1 + \frac{2}{-1} = \frac{2}{-1} \)
\( 1 - 2 = -2 \)
\( -1 \neq -2 \) (Not a solution)

3. **Equation:**
\( 1 + \frac{3}{x - 3} = \frac{2}{x - 3} \)
Substitute \( x = 2 \):
\( 1 + \frac{3}{2 - 3} = \frac{2}{2 - 3} \)
\( 1 + \frac{3}{-1} = \frac{2}{-1} \)
\( 1 - 3 = -2 \)
\( -2 = -2 \) (This is a solution)

4. **Equation:**
\( 1 + \frac{1}{x - 3} = 2x - 3 \)
Substitute \( x = 2 \):
\( 1 + \frac{1}{2 - 3} = 2(2) - 3 \)
\( 1 + \frac{1}{-1} = 4 - 3 \)
\( 1 - 1 = 1 \)
\( 0 \neq 1 \) (Not a solution)

From the evaluations, the correct equation that has a solution of \( x = 2 \) is:

**1 + \frac{3}{x - 3} = \frac{2}{x - 3}** (Equation 3)