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Simplifying 4x + 30 = 2k(x + 1) Reorder the terms: 30 + 4x = 2k(x + 1) Reorder the terms: 30 + 4x = 2k(1 + x) 30 + 4x = (1 * 2k + x * 2k) 30 + 4x = (2k + 2kx) Solving 30 + 4x = 2k + 2kx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2kx' to each side of the equation. 30 + -2kx + 4x = 2k + 2kx + -2kx Combine like terms: 2kx + -2kx = 0 30 + -2kx + 4x = 2k + 0 30 + -2kx + 4x = 2k Add '-30' to each side of the equation. 30 + -2kx + -30 + 4x = -30 + 2k Reorder the terms: 30 + -30 + -2kx + 4x = -30 + 2k Combine like terms: 30 + -30 = 0 0 + -2kx + 4x = -30 + 2k -2kx + 4x = -30 + 2k Reorder the terms: 30 + -2k + -2kx + 4x = -30 + 2k + 30 + -2k Reorder the terms: 30 + -2k + -2kx + 4x = -30 + 30 + 2k + -2k Combine like terms: -30 + 30 = 0 30 + -2k + -2kx + 4x = 0 + 2k + -2k 30 + -2k + -2kx + 4x = 2k + -2k Combine like terms: 2k + -2k = 0 30 + -2k + -2kx + 4x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -1k + -1kx + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -1k + -1kx + 2x)' equal to zero and attempt to solve: Simplifying 15 + -1k + -1kx + 2x = 0 Solving 15 + -1k + -1kx + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -1k + -1kx + -15 + 2x = 0 + -15 Reorder the terms: 15 + -15 + -1k + -1kx + 2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1k + -1kx + 2x = 0 + -15 -1k + -1kx + 2x = 0 + -15 Combine like terms: 0 + -15 = -15 -1k + -1kx + 2x = -15 Add 'k' to each side of the equation. -1k + -1kx + k + 2x = -15 + k Reorder the terms: -1k + k + -1kx + 2x = -15 + k Combine like terms: -1k + k = 0 0 + -1kx + 2x = -15 + k -1kx + 2x = -15 + k 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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