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Solve for z. Assume the equation has a solution for z. {:[-4z+1=bz+c],[z=◻++_]:}

Solve for z z .\newlineAssume the equation has a solution for z z .\newline−4z+1=bz+cz=□ \begin{array}{l} -4 z+1=b z+c \\ z=\square \end{array}

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Full solution

Q. Solve for z z .\newlineAssume the equation has a solution for z z .\newline−4z+1=bz+cz=□ \begin{array}{l} -4 z+1=b z+c \\ z=\square \end{array}
  1. Identify system and unknown variable: Identify the system of equations and the unknown variable to solve for.\newlineThe system of equations is:\newline−4z+1=bz+c-4z + 1 = bz + c\newlineWe need to solve for zz.
  2. Combine like terms: Combine like terms by moving all terms involving zz to one side of the equation.\newlineAdd 4z4z to both sides to get zz terms on one side:\newline−4z+1+4z=bz+c+4z-4z + 1 + 4z = bz + c + 4z\newlineThis simplifies to:\newline1=(b+4)z+c1 = (b + 4)z + c
  3. Isolate the term with z: Isolate the term with z.\newlineSubtract cc from both sides to get:\newline1−c=(b+4)z1 - c = (b + 4)z
  4. Divide both sides to solve for zz: Divide both sides by (b+4)(b + 4) to solve for zz.z=1−cb+4z = \frac{1 - c}{b + 4}

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