Final answer:
The equation with exactly one solution is 2x + 3 = 5x - 7. The correct answer is option B .
Step-by-step explanation:
To find the equation with exactly one solution, we need to determine which equation has only one value for x that satisfies the equation. Let's examine each option:
a) 2x + 3 = 5x - 7
Subtract 2x from both sides to isolate the variable: 3 = 3x - 7
Add 7 to both sides: 10 = 3x
Divide both sides by 3: x = 10/3
This equation has only one solution.
b) 3x + 4 = 3x + 4
This equation has infinitely many solutions because the variables cancel out, resulting in a true statement.
c) 4x - 2 = 2(2x + 1)
First, distribute the 2 on the right side: 4x - 2 = 4x + 2
Subtract 4x from both sides to isolate the variable: -2 = 2
This equation has no solution.
d) x - 5 = x - 5
This equation has infinitely many solutions because the variables cancel out, resulting in a true statement.
Therefore, the equation with exactly one solution is a) 2x + 3 = 5x - 7.