Solve linear equations with variables on both sides and interpret special cases.
Recognize special solution cases
Problem
Eliminate the variable terms from \(4x~+~7~=~4x~-~2\). State the resulting constant equality and classify the equation as having \(\text{one}~\text{solution}\), \(\text{no}~\text{solution}\), or infinitely many solutions.
Big Picture
What this problem is really about
Subtract the identical variable expression from both sides and inspect what remains. If the variables disappear, the resulting constant statement—not an assumed value of zero—determines the solution case. A true constant equality would allow every x, while a false one means no value can satisfy the original equation.
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