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Simplifying (4x + 7)(r + -1) = -1(25r + -25) Reorder the terms: (7 + 4x)(r + -1) = -1(25r + -25) Reorder the terms: (7 + 4x)(-1 + r) = -1(25r + -25) Multiply (7 + 4x) * (-1 + r) (7(-1 + r) + 4x * (-1 + r)) = -1(25r + -25) ((-1 * 7 + r * 7) + 4x * (-1 + r)) = -1(25r + -25) ((-7 + 7r) + 4x * (-1 + r)) = -1(25r + -25) (-7 + 7r + (-1 * 4x + r * 4x)) = -1(25r + -25) Reorder the terms: (-7 + 7r + (4rx + -4x)) = -1(25r + -25) (-7 + 7r + (4rx + -4x)) = -1(25r + -25) (-7 + 7r + 4rx + -4x) = -1(25r + -25) Reorder the terms: -7 + 7r + 4rx + -4x = -1(-25 + 25r) -7 + 7r + 4rx + -4x = (-25 * -1 + 25r * -1) -7 + 7r + 4rx + -4x = (25 + -25r) Solving -7 + 7r + 4rx + -4x = 25 + -25r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '25r' to each side of the equation. -7 + 7r + 4rx + 25r + -4x = 25 + -25r + 25r Reorder the terms: -7 + 7r + 25r + 4rx + -4x = 25 + -25r + 25r Combine like terms: 7r + 25r = 32r -7 + 32r + 4rx + -4x = 25 + -25r + 25r Combine like terms: -25r + 25r = 0 -7 + 32r + 4rx + -4x = 25 + 0 -7 + 32r + 4rx + -4x = 25 Add '7' to each side of the equation. -7 + 32r + 4rx + 7 + -4x = 25 + 7 Reorder the terms: -7 + 7 + 32r + 4rx + -4x = 25 + 7 Combine like terms: -7 + 7 = 0 0 + 32r + 4rx + -4x = 25 + 7 32r + 4rx + -4x = 25 + 7 Combine like terms: 25 + 7 = 32 32r + 4rx + -4x = 32 Add '4x' to each side of the equation. 32r + 4rx + -4x + 4x = 32 + 4x Combine like terms: -4x + 4x = 0 32r + 4rx + 0 = 32 + 4x 32r + 4rx = 32 + 4x Reorder the terms: -32 + 32r + 4rx + -4x = 32 + 4x + -32 + -4x Reorder the terms: -32 + 32r + 4rx + -4x = 32 + -32 + 4x + -4x Combine like terms: 32 + -32 = 0 -32 + 32r + 4rx + -4x = 0 + 4x + -4x -32 + 32r + 4rx + -4x = 4x + -4x Combine like terms: 4x + -4x = 0 -32 + 32r + 4rx + -4x = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 8r + rx + -1x) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 8r + rx + -1x)' equal to zero and attempt to solve: Simplifying -8 + 8r + rx + -1x = 0 Solving -8 + 8r + rx + -1x = 0 Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8r + rx + 8 + -1x = 0 + 8 Reorder the terms: -8 + 8 + 8r + rx + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8r + rx + -1x = 0 + 8 8r + rx + -1x = 0 + 8 Combine like terms: 0 + 8 = 8 8r + rx + -1x = 8 Add 'x' to each side of the equation. 8r + rx + -1x + x = 8 + x Combine like terms: -1x + x = 0 8r + rx + 0 = 8 + x 8r + rx = 8 + x 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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