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Simplifying 7[4w + -2(3w + 8)] + -1w = 4(3w + -2) + 6 Reorder the terms: 7[4w + -2(8 + 3w)] + -1w = 4(3w + -2) + 6 7[4w + (8 * -2 + 3w * -2)] + -1w = 4(3w + -2) + 6 7[4w + (-16 + -6w)] + -1w = 4(3w + -2) + 6 Reorder the terms: 7[-16 + 4w + -6w] + -1w = 4(3w + -2) + 6 Combine like terms: 4w + -6w = -2w 7[-16 + -2w] + -1w = 4(3w + -2) + 6 [-16 * 7 + -2w * 7] + -1w = 4(3w + -2) + 6 [-112 + -14w] + -1w = 4(3w + -2) + 6 Combine like terms: -14w + -1w = -15w -112 + -15w = 4(3w + -2) + 6 Reorder the terms: -112 + -15w = 4(-2 + 3w) + 6 -112 + -15w = (-2 * 4 + 3w * 4) + 6 -112 + -15w = (-8 + 12w) + 6 Reorder the terms: -112 + -15w = -8 + 6 + 12w Combine like terms: -8 + 6 = -2 -112 + -15w = -2 + 12w Solving -112 + -15w = -2 + 12w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12w' to each side of the equation. -112 + -15w + -12w = -2 + 12w + -12w Combine like terms: -15w + -12w = -27w -112 + -27w = -2 + 12w + -12w Combine like terms: 12w + -12w = 0 -112 + -27w = -2 + 0 -112 + -27w = -2 Add '112' to each side of the equation. -112 + 112 + -27w = -2 + 112 Combine like terms: -112 + 112 = 0 0 + -27w = -2 + 112 -27w = -2 + 112 Combine like terms: -2 + 112 = 110 -27w = 110 Divide each side by '-27'. w = -4.074074074 Simplifying w = -4.074074074
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