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Solve for x. Assume the equation has a solution for x. {:[19 x+rx=-37 x+w],[x=]:}

Solve for x x .\newlineAssume the equation has a solution for x x .\newline19x+rx=−37x+wx=□ \begin{array}{l} 19 x+r x=-37 x+w \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newlineAssume the equation has a solution for x x .\newline19x+rx=−37x+wx=□ \begin{array}{l} 19 x+r x=-37 x+w \\ x=\square \end{array}
  1. Combine like terms: Combine like terms on the left side of the equation. \newline19x+rx19x + rx can be combined because they are like terms.\newline(19+r)x=−37x+w(19 + r)x = -37x + w
  2. Move term involving x: Move the term involving x on the right side to the left side by adding 37x37x to both sides.\newline(19+r)x+37x=w(19 + r)x + 37x = w\newlineCombine the x terms.\newline(19+r+37)x=w(19 + r + 37)x = w\newline(56+r)x=w(56 + r)x = w
  3. Combine xx terms: Isolate xx by dividing both sides by the coefficient (56+r56 + r).\newlinex=w56+rx = \frac{w}{56 + r}\newlineCheck that (56+r)(56 + r) is not equal to zero to avoid division by zero.

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