To determine which of the given equations has exactly one solution, we can analyze each option:
A) \(3x + 4 = 4x + 3\)
Subtract \(3x\) from both sides: \[ 4 = x + 3 \] Subtract 3 from both sides: \[ 1 = x \] This equation has exactly one solution: \(x = 1\).
B) \(3x + 4 = 3x + 4\)
This simplifies to \(0 = 0\), which is true for any value of \(x\). Therefore, this equation has infinitely many solutions.
C) \(4x + 3 = 4x + 3\)
Similar to option B, this simplifies to \(0 = 0\), which is also true for any value of \(x\). Thus, this equation has infinitely many solutions.
D) \(3x + 4 = 3x + 3\)
Subtract \(3x\) from both sides: \[ 4 = 3 \] This statement is false, meaning there are no solutions.
After analyzing all options, the only equation with exactly one solution is:
A) \(3x + 4 = 4x + 3\)
1 answer