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Simplifying 19 + -1(5w + -2) + -7(w + 3) + 6z = 0 Reorder the terms: 19 + -1(-2 + 5w) + -7(w + 3) + 6z = 0 19 + (-2 * -1 + 5w * -1) + -7(w + 3) + 6z = 0 19 + (2 + -5w) + -7(w + 3) + 6z = 0 Reorder the terms: 19 + 2 + -5w + -7(3 + w) + 6z = 0 19 + 2 + -5w + (3 * -7 + w * -7) + 6z = 0 19 + 2 + -5w + (-21 + -7w) + 6z = 0 Reorder the terms: 19 + 2 + -21 + -5w + -7w + 6z = 0 Combine like terms: 19 + 2 = 21 21 + -21 + -5w + -7w + 6z = 0 Combine like terms: 21 + -21 = 0 0 + -5w + -7w + 6z = 0 -5w + -7w + 6z = 0 Combine like terms: -5w + -7w = -12w -12w + 6z = 0 Solving -12w + 6z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6z' to each side of the equation. -12w + 6z + -6z = 0 + -6z Combine like terms: 6z + -6z = 0 -12w + 0 = 0 + -6z -12w = 0 + -6z Remove the zero: -12w = -6z Divide each side by '-12'. w = 0.5z Simplifying w = 0.5z
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