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Simplifying Px + 76 = Qx + 76 Reorder the terms: 76 + xP = Qx + 76 Reorder the terms: 76 + xP = 76 + xQ Add '-76' to each side of the equation. 76 + -76 + xP = 76 + -76 + xQ Combine like terms: 76 + -76 = 0 0 + xP = 76 + -76 + xQ xP = 76 + -76 + xQ Combine like terms: 76 + -76 = 0 xP = 0 + xQ xP = xQ Solving xP = xQ Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1xQ' to each side of the equation. xP + -1xQ = xQ + -1xQ Combine like terms: xQ + -1xQ = 0 xP + -1xQ = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(P + -1Q) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(P + -1Q)' equal to zero and attempt to solve: Simplifying P + -1Q = 0 Solving P + -1Q = 0 Move all terms containing x to the left, all other terms to the right. Add '-1P' to each side of the equation. P + -1P + -1Q = 0 + -1P Combine like terms: P + -1P = 0 0 + -1Q = 0 + -1P -1Q = 0 + -1P Remove the zero: -1Q = -1P Add 'Q' to each side of the equation. -1Q + Q = -1P + Q Combine like terms: -1Q + Q = 0 0 = -1P + Q Simplifying 0 = -1P + Q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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