To determine which of the given equations has no solution, let's analyze each one:
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\(3X + 4 = 3X + 4\)
This equation is true for all values of \(X\) because both sides are identical. Therefore, it has infinitely many solutions. -
\(4X + 3 = 3X + 3\)
If we subtract \(3X\) from both sides, we get: \[ 4X - 3X + 3 = 3 \] Simplifying yields: \[ X + 3 = 3 \implies X = 0 \] This equation has exactly one solution (X = 0). -
\(3X + 4 = 3X + 3\)
Subtracting \(3X\) from both sides gives us: \[ 4 = 3 \] This statement is false, indicating there are no values of \(X\) that satisfy this equation. Therefore, it has no solution. -
\(3X + 4 = 4X + 3\)
Rearranging gives us: \[ 3X + 4 - 4X = 3 \implies -X + 4 = 3 \] Simplifying yields: \[ -X = -1 \implies X = 1 \] This equation has exactly one solution (X = 1).
In summary, the equation \(3X + 4 = 3X + 3\) is the example of an equation with no solution.