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Solve for x. Assume the equation has a solution for x. {:[a*(5-x)=bx-8],[x=◻+∓-x]:}

Solve for x x .\newlineAssume the equation has a solution for x x .\newlinea⋅(5−x)=bx−8x=□ \begin{array}{l} a \cdot(5-x)=b x-8 \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newlineAssume the equation has a solution for x x .\newlinea⋅(5−x)=bx−8x=□ \begin{array}{l} a \cdot(5-x)=b x-8 \\ x=\square \end{array}
  1. Identify the system: Identify the given system of equations.\newlineWe have the system:\newlinea⋅(5−x)=bx−8a\cdot(5-x) = bx - 8\newlinex=□±−xx = \square \pm \sqrt{-x}
  2. Simplify the first equation: Simplify the first equation by distributing aa.a⋅5−a⋅x=bx−8a \cdot 5 - a \cdot x = bx - 85a−ax=bx−85a - ax = bx - 8
  3. Move terms involving x: Move all terms involving x to one side of the equation.\newline55a - ax - bx = −8-8\newlineCombine like terms.\newline55a - (a + b)x = −8-8
  4. Combine like terms: Isolate xx by dividing both sides by −(a+b)- (a + b).\newlinex=−8−(a+b)x = \frac{-8}{-(a + b)}\newlineSimplify the division.\newlinex=8(a+b)x = \frac{8}{(a + b)}
  5. Isolate xx: The second equation x=□±∓−xx = \square \pm \mp -x does not make sense as written. It seems to be an error or a misinterpretation of the problem. We cannot proceed with this equation.

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