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8x+5=bx78x + 5 = bx - 7 \newlineIn the equation shown above, b is a constant. \newlineFor what value of b does the equation have no solutions? \newline(A) 8-8 \newline(B) 7-7 \newline(C) 55 \newline(D) 88

Full solution

Q. 8x+5=bx78x + 5 = bx - 7 \newlineIn the equation shown above, b is a constant. \newlineFor what value of b does the equation have no solutions? \newline(A) 8-8 \newline(B) 7-7 \newline(C) 55 \newline(D) 88
  1. Set Equation: Step Title: Set the Equation\newlineConcise Step Description: Set the given equation in the standard form by moving all terms to one side.\newlineCalculation: Subtract bxbx from both sides to get 8xbx+5+7=08x - bx + 5 + 7 = 0.\newlineMath Error Check:
  2. Combine Like Terms: Step Title: Combine Like Terms\newlineConcise Step Description: Combine like terms to simplify the equation.\newlineCalculation: Combine the xx terms and the constant terms to get (8b)x+12=0(8 - b)x + 12 = 0.\newlineMath Error Check:
  3. Isolate Variable Term: Step Title: Isolate the Variable Term\newlineConcise Step Description: Isolate the variable term to solve for xx.\newlineCalculation: Subtract 1212 from both sides to get (8b)x=12(8 - b)x = -12.\newlineMath Error Check:
  4. Solve for x: Step Title: Solve for x\newlineConcise Step Description: Divide both sides by the coefficient of xx to solve for xx.\newlineCalculation: x=128bx = -\frac{12}{8 - b}.\newlineMath Error Check: