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How many solutions does this equation have?\newline−4+4z=5z-4 + 4z = 5z\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions\newline

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Q. How many solutions does this equation have?\newline−4+4z=5z-4 + 4z = 5z\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions\newline
  1. Isolate variable zz: Isolate the variable zz on one side of the equation. −4+4z=5z\,-4 + 4z = 5z Subtract 4z4z from both sides to get: −4=5z−4z\,-4 = 5z - 4z
  2. Simplify equation: Simplify the right side of the equation by combining like terms. \newline−4=5z−4z-4 = 5z - 4z\newline−4=z-4 = z
  3. Check solution validity: Check if the solution is valid.\newlineSubstitute zz with –4–4 into the original equation to verify:\newline–4+4(–4)=5(–4)–4 + 4(–4) = 5(–4)\newline–4−16=−20–4 - 16 = -20\newline–20=–20–20 = –20\newlineThis shows that the solution z=–4z = –4 satisfies the original equation.
  4. Determine number of solutions: Determine the number of solutions. Since we found a specific value for zz that satisfies the equation, there is only 11 solution.

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