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Simplifying 3(yk + -2) + -4(5k + 1) = 2 + -2(k + 3) Reorder the terms: 3(-2 + ky) + -4(5k + 1) = 2 + -2(k + 3) (-2 * 3 + ky * 3) + -4(5k + 1) = 2 + -2(k + 3) (-6 + 3ky) + -4(5k + 1) = 2 + -2(k + 3) Reorder the terms: -6 + 3ky + -4(1 + 5k) = 2 + -2(k + 3) -6 + 3ky + (1 * -4 + 5k * -4) = 2 + -2(k + 3) -6 + 3ky + (-4 + -20k) = 2 + -2(k + 3) Reorder the terms: -6 + -4 + -20k + 3ky = 2 + -2(k + 3) Combine like terms: -6 + -4 = -10 -10 + -20k + 3ky = 2 + -2(k + 3) Reorder the terms: -10 + -20k + 3ky = 2 + -2(3 + k) -10 + -20k + 3ky = 2 + (3 * -2 + k * -2) -10 + -20k + 3ky = 2 + (-6 + -2k) Combine like terms: 2 + -6 = -4 -10 + -20k + 3ky = -4 + -2k Solving -10 + -20k + 3ky = -4 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. -10 + -20k + 2k + 3ky = -4 + -2k + 2k Combine like terms: -20k + 2k = -18k -10 + -18k + 3ky = -4 + -2k + 2k Combine like terms: -2k + 2k = 0 -10 + -18k + 3ky = -4 + 0 -10 + -18k + 3ky = -4 Add '10' to each side of the equation. -10 + -18k + 10 + 3ky = -4 + 10 Reorder the terms: -10 + 10 + -18k + 3ky = -4 + 10 Combine like terms: -10 + 10 = 0 0 + -18k + 3ky = -4 + 10 -18k + 3ky = -4 + 10 Combine like terms: -4 + 10 = 6 -18k + 3ky = 6 Reorder the terms: -6 + -18k + 3ky = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -18k + 3ky = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -6k + ky) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -6k + ky)' equal to zero and attempt to solve: Simplifying -2 + -6k + ky = 0 Solving -2 + -6k + ky = 0 Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -6k + 2 + ky = 0 + 2 Reorder the terms: -2 + 2 + -6k + ky = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6k + ky = 0 + 2 -6k + ky = 0 + 2 Combine like terms: 0 + 2 = 2 -6k + ky = 2 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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