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Simplifying 33 = 12r + -3z(9 + -1r) 33 = 12r + (9 * -3z + -1r * -3z) Reorder the terms: 33 = 12r + (3rz + -27z) 33 = 12r + (3rz + -27z) Solving 33 = 12r + 3rz + -27z Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. 33 + -12r = 12r + 3rz + -12r + -27z Reorder the terms: 33 + -12r = 12r + -12r + 3rz + -27z Combine like terms: 12r + -12r = 0 33 + -12r = 0 + 3rz + -27z 33 + -12r = 3rz + -27z Add '-3rz' to each side of the equation. 33 + -12r + -3rz = 3rz + -3rz + -27z Combine like terms: 3rz + -3rz = 0 33 + -12r + -3rz = 0 + -27z 33 + -12r + -3rz = -27z Add '-33' to each side of the equation. 33 + -12r + -33 + -3rz = -33 + -27z Reorder the terms: 33 + -33 + -12r + -3rz = -33 + -27z Combine like terms: 33 + -33 = 0 0 + -12r + -3rz = -33 + -27z -12r + -3rz = -33 + -27z Reorder the terms: 33 + -12r + -3rz + 27z = -33 + -27z + 33 + 27z Reorder the terms: 33 + -12r + -3rz + 27z = -33 + 33 + -27z + 27z Combine like terms: -33 + 33 = 0 33 + -12r + -3rz + 27z = 0 + -27z + 27z 33 + -12r + -3rz + 27z = -27z + 27z Combine like terms: -27z + 27z = 0 33 + -12r + -3rz + 27z = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -4r + -1rz + 9z) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -4r + -1rz + 9z)' equal to zero and attempt to solve: Simplifying 11 + -4r + -1rz + 9z = 0 Solving 11 + -4r + -1rz + 9z = 0 Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -4r + -1rz + -11 + 9z = 0 + -11 Reorder the terms: 11 + -11 + -4r + -1rz + 9z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4r + -1rz + 9z = 0 + -11 -4r + -1rz + 9z = 0 + -11 Combine like terms: 0 + -11 = -11 -4r + -1rz + 9z = -11 Add '-9z' to each side of the equation. -4r + -1rz + 9z + -9z = -11 + -9z Combine like terms: 9z + -9z = 0 -4r + -1rz + 0 = -11 + -9z -4r + -1rz = -11 + -9z 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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