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Simplifying ifp(x) = 2x + 5findp(x) + p(-1x) Multiply fip * x fipx = 2x + 5findp(x) + p(-1x) Multiply dfinp * x fipx = 2x + 5dfinpx + p(-1x) Remove parenthesis around (-1x) fipx = 2x + 5dfinpx + p * -1x Reorder the terms for easier multiplication: fipx = 2x + 5dfinpx + -1p * x Multiply p * x fipx = 2x + 5dfinpx + -1px Reorder the terms: fipx = 5dfinpx + -1px + 2x Solving fipx = 5dfinpx + -1px + 2x Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-5dfinpx' to each side of the equation. -5dfinpx + fipx = 5dfinpx + -1px + -5dfinpx + 2x Reorder the terms: -5dfinpx + fipx = 5dfinpx + -5dfinpx + -1px + 2x Combine like terms: 5dfinpx + -5dfinpx = 0 -5dfinpx + fipx = 0 + -1px + 2x -5dfinpx + fipx = -1px + 2x Reorder the terms: -5dfinpx + fipx + px + -2x = -1px + px + 2x + -2x Combine like terms: -1px + px = 0 -5dfinpx + fipx + px + -2x = 0 + 2x + -2x -5dfinpx + fipx + px + -2x = 2x + -2x Combine like terms: 2x + -2x = 0 -5dfinpx + fipx + px + -2x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5dfinp + fip + p + -2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing f to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5dfinp + fip + p + -2)' equal to zero and attempt to solve: Simplifying -5dfinp + fip + p + -2 = 0 Reorder the terms: -2 + -5dfinp + fip + p = 0 Solving -2 + -5dfinp + fip + p = 0 Move all terms containing f to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -5dfinp + fip + 2 + p = 0 + 2 Reorder the terms: -2 + 2 + -5dfinp + fip + p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5dfinp + fip + p = 0 + 2 -5dfinp + fip + p = 0 + 2 Combine like terms: 0 + 2 = 2 -5dfinp + fip + p = 2 Add '-1p' to each side of the equation. -5dfinp + fip + p + -1p = 2 + -1p Combine like terms: p + -1p = 0 -5dfinp + fip + 0 = 2 + -1p -5dfinp + fip = 2 + -1p 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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