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Simplifying -1x = (5x + 3)(3k + 1) Reorder the terms: -1x = (3 + 5x)(3k + 1) Reorder the terms: -1x = (3 + 5x)(1 + 3k) Multiply (3 + 5x) * (1 + 3k) -1x = (3(1 + 3k) + 5x * (1 + 3k)) -1x = ((1 * 3 + 3k * 3) + 5x * (1 + 3k)) -1x = ((3 + 9k) + 5x * (1 + 3k)) -1x = (3 + 9k + (1 * 5x + 3k * 5x)) Reorder the terms: -1x = (3 + 9k + (15kx + 5x)) -1x = (3 + 9k + (15kx + 5x)) -1x = (3 + 9k + 15kx + 5x) Solving -1x = 3 + 9k + 15kx + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15kx' to each side of the equation. -15kx + -1x = 3 + 9k + 15kx + -15kx + 5x Combine like terms: 15kx + -15kx = 0 -15kx + -1x = 3 + 9k + 0 + 5x -15kx + -1x = 3 + 9k + 5x Add '-5x' to each side of the equation. -15kx + -1x + -5x = 3 + 9k + 5x + -5x Combine like terms: -1x + -5x = -6x -15kx + -6x = 3 + 9k + 5x + -5x Combine like terms: 5x + -5x = 0 -15kx + -6x = 3 + 9k + 0 -15kx + -6x = 3 + 9k Reorder the terms: -3 + -9k + -15kx + -6x = 3 + 9k + -3 + -9k Reorder the terms: -3 + -9k + -15kx + -6x = 3 + -3 + 9k + -9k Combine like terms: 3 + -3 = 0 -3 + -9k + -15kx + -6x = 0 + 9k + -9k -3 + -9k + -15kx + -6x = 9k + -9k Combine like terms: 9k + -9k = 0 -3 + -9k + -15kx + -6x = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 3k + 5kx + 2x) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(1 + 3k + 5kx + 2x)' equal to zero and attempt to solve: Simplifying 1 + 3k + 5kx + 2x = 0 Solving 1 + 3k + 5kx + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 3k + 5kx + -1 + 2x = 0 + -1 Reorder the terms: 1 + -1 + 3k + 5kx + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3k + 5kx + 2x = 0 + -1 3k + 5kx + 2x = 0 + -1 Combine like terms: 0 + -1 = -1 3k + 5kx + 2x = -1 Add '-3k' to each side of the equation. 3k + 5kx + -3k + 2x = -1 + -3k Reorder the terms: 3k + -3k + 5kx + 2x = -1 + -3k Combine like terms: 3k + -3k = 0 0 + 5kx + 2x = -1 + -3k 5kx + 2x = -1 + -3k 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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