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Solve for x. Assume the equation has a solution for x. {:[ax+3x=bx+5],[x=◻]:}

Solve for x x .\newlineAssume the equation has a solution for x x .\newlineax+3x=bx+5x=□ \begin{array}{l} a x+3 x=b x+5 \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newlineAssume the equation has a solution for x x .\newlineax+3x=bx+5x=□ \begin{array}{l} a x+3 x=b x+5 \\ x=\square \end{array}
  1. Combine like terms: Combine like terms on the left side of the equation. \newlineax+3xax + 3x can be combined because they are like terms (both have the variable xx).\newline(ax+3x)=a⋅x+3⋅x=(a+3)x(ax + 3x) = a \cdot x + 3 \cdot x = (a + 3)x\newlineNow the equation looks like: (a+3)x=bx+5(a + 3)x = bx + 5
  2. Subtract bxbx from both sides: Subtract bxbx from both sides to get all terms with xx on one side.\newline(a+3)x−bx=bx+5−bx(a + 3)x - bx = bx + 5 - bx\newlineThis simplifies to: (a+3)x−bx=5(a + 3)x - bx = 5
  3. Combine like terms: Combine like terms on the left side of the equation.\newline(a+3)x−bx(a + 3)x - bx can be combined because they are like terms (both have the variable xx).\newline(a+3−b)x=5(a + 3 - b)x = 5\newlineNow the equation looks like: (a+3−b)x=5(a + 3 - b)x = 5
  4. Divide both sides: Divide both sides by the coefficient of xx, which is (a+3−b)(a + 3 - b).\newlinex=5(a+3−b)x = \frac{5}{(a + 3 - b)}\newlineThis gives us the value of xx in terms of aa and bb.

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