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Simplifying 5(2w + -1) + 6(3w + -4) = 111 Reorder the terms: 5(-1 + 2w) + 6(3w + -4) = 111 (-1 * 5 + 2w * 5) + 6(3w + -4) = 111 (-5 + 10w) + 6(3w + -4) = 111 Reorder the terms: -5 + 10w + 6(-4 + 3w) = 111 -5 + 10w + (-4 * 6 + 3w * 6) = 111 -5 + 10w + (-24 + 18w) = 111 Reorder the terms: -5 + -24 + 10w + 18w = 111 Combine like terms: -5 + -24 = -29 -29 + 10w + 18w = 111 Combine like terms: 10w + 18w = 28w -29 + 28w = 111 Solving -29 + 28w = 111 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + 28w = 111 + 29 Combine like terms: -29 + 29 = 0 0 + 28w = 111 + 29 28w = 111 + 29 Combine like terms: 111 + 29 = 140 28w = 140 Divide each side by '28'. w = 5 Simplifying w = 5
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