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Simplifying 5(6w + -3) + -7 = 17 + 3w + -5(2w + 1) Reorder the terms: 5(-3 + 6w) + -7 = 17 + 3w + -5(2w + 1) (-3 * 5 + 6w * 5) + -7 = 17 + 3w + -5(2w + 1) (-15 + 30w) + -7 = 17 + 3w + -5(2w + 1) Reorder the terms: -15 + -7 + 30w = 17 + 3w + -5(2w + 1) Combine like terms: -15 + -7 = -22 -22 + 30w = 17 + 3w + -5(2w + 1) Reorder the terms: -22 + 30w = 17 + 3w + -5(1 + 2w) -22 + 30w = 17 + 3w + (1 * -5 + 2w * -5) -22 + 30w = 17 + 3w + (-5 + -10w) Reorder the terms: -22 + 30w = 17 + -5 + 3w + -10w Combine like terms: 17 + -5 = 12 -22 + 30w = 12 + 3w + -10w Combine like terms: 3w + -10w = -7w -22 + 30w = 12 + -7w Solving -22 + 30w = 12 + -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. -22 + 30w + 7w = 12 + -7w + 7w Combine like terms: 30w + 7w = 37w -22 + 37w = 12 + -7w + 7w Combine like terms: -7w + 7w = 0 -22 + 37w = 12 + 0 -22 + 37w = 12 Add '22' to each side of the equation. -22 + 22 + 37w = 12 + 22 Combine like terms: -22 + 22 = 0 0 + 37w = 12 + 22 37w = 12 + 22 Combine like terms: 12 + 22 = 34 37w = 34 Divide each side by '37'. w = 0.9189189189 Simplifying w = 0.9189189189
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