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Simplifying 2 + 6(2x + -1) = 4(Px + Q) Reorder the terms: 2 + 6(-1 + 2x) = 4(Px + Q) 2 + (-1 * 6 + 2x * 6) = 4(Px + Q) 2 + (-6 + 12x) = 4(Px + Q) Combine like terms: 2 + -6 = -4 -4 + 12x = 4(Px + Q) Reorder the terms: -4 + 12x = 4(Q + xP) -4 + 12x = (Q * 4 + xP * 4) -4 + 12x = (4Q + 4xP) Solving -4 + 12x = 4Q + 4xP Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4xP' to each side of the equation. -4 + 12x + -4xP = 4Q + 4xP + -4xP Combine like terms: 4xP + -4xP = 0 -4 + 12x + -4xP = 4Q + 0 -4 + 12x + -4xP = 4Q Add '4' to each side of the equation. -4 + 12x + 4 + -4xP = 4 + 4Q Reorder the terms: -4 + 4 + 12x + -4xP = 4 + 4Q Combine like terms: -4 + 4 = 0 0 + 12x + -4xP = 4 + 4Q 12x + -4xP = 4 + 4Q Reorder the terms: -4 + -4Q + 12x + -4xP = 4 + 4Q + -4 + -4Q Reorder the terms: -4 + -4Q + 12x + -4xP = 4 + -4 + 4Q + -4Q Combine like terms: 4 + -4 = 0 -4 + -4Q + 12x + -4xP = 0 + 4Q + -4Q -4 + -4Q + 12x + -4xP = 4Q + -4Q Combine like terms: 4Q + -4Q = 0 -4 + -4Q + 12x + -4xP = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -1Q + 3x + -1xP) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1Q + 3x + -1xP)' equal to zero and attempt to solve: Simplifying -1 + -1Q + 3x + -1xP = 0 Solving -1 + -1Q + 3x + -1xP = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1Q + 3x + 1 + -1xP = 0 + 1 Reorder the terms: -1 + 1 + -1Q + 3x + -1xP = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1Q + 3x + -1xP = 0 + 1 -1Q + 3x + -1xP = 0 + 1 Combine like terms: 0 + 1 = 1 -1Q + 3x + -1xP = 1 Add 'Q' to each side of the equation. -1Q + 3x + Q + -1xP = 1 + Q Reorder the terms: -1Q + Q + 3x + -1xP = 1 + Q Combine like terms: -1Q + Q = 0 0 + 3x + -1xP = 1 + Q 3x + -1xP = 1 + Q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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