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Simplifying 9w + -7 = 4(7w + 1) + -3(1 + 7w) Reorder the terms: -7 + 9w = 4(7w + 1) + -3(1 + 7w) Reorder the terms: -7 + 9w = 4(1 + 7w) + -3(1 + 7w) -7 + 9w = (1 * 4 + 7w * 4) + -3(1 + 7w) -7 + 9w = (4 + 28w) + -3(1 + 7w) -7 + 9w = 4 + 28w + (1 * -3 + 7w * -3) -7 + 9w = 4 + 28w + (-3 + -21w) Reorder the terms: -7 + 9w = 4 + -3 + 28w + -21w Combine like terms: 4 + -3 = 1 -7 + 9w = 1 + 28w + -21w Combine like terms: 28w + -21w = 7w -7 + 9w = 1 + 7w Solving -7 + 9w = 1 + 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. -7 + 9w + -7w = 1 + 7w + -7w Combine like terms: 9w + -7w = 2w -7 + 2w = 1 + 7w + -7w Combine like terms: 7w + -7w = 0 -7 + 2w = 1 + 0 -7 + 2w = 1 Add '7' to each side of the equation. -7 + 7 + 2w = 1 + 7 Combine like terms: -7 + 7 = 0 0 + 2w = 1 + 7 2w = 1 + 7 Combine like terms: 1 + 7 = 8 2w = 8 Divide each side by '2'. w = 4 Simplifying w = 4
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