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Simplifying -7(1 + -4z) + 2 = 13(2z + -3) + 2 (1 * -7 + -4z * -7) + 2 = 13(2z + -3) + 2 (-7 + 28z) + 2 = 13(2z + -3) + 2 Reorder the terms: -7 + 2 + 28z = 13(2z + -3) + 2 Combine like terms: -7 + 2 = -5 -5 + 28z = 13(2z + -3) + 2 Reorder the terms: -5 + 28z = 13(-3 + 2z) + 2 -5 + 28z = (-3 * 13 + 2z * 13) + 2 -5 + 28z = (-39 + 26z) + 2 Reorder the terms: -5 + 28z = -39 + 2 + 26z Combine like terms: -39 + 2 = -37 -5 + 28z = -37 + 26z Solving -5 + 28z = -37 + 26z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-26z' to each side of the equation. -5 + 28z + -26z = -37 + 26z + -26z Combine like terms: 28z + -26z = 2z -5 + 2z = -37 + 26z + -26z Combine like terms: 26z + -26z = 0 -5 + 2z = -37 + 0 -5 + 2z = -37 Add '5' to each side of the equation. -5 + 5 + 2z = -37 + 5 Combine like terms: -5 + 5 = 0 0 + 2z = -37 + 5 2z = -37 + 5 Combine like terms: -37 + 5 = -32 2z = -32 Divide each side by '2'. z = -16 Simplifying z = -16
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