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Simplifying 3(2w + -7) + -1w = 5(w + -1) + 16(2w + 3) Reorder the terms: 3(-7 + 2w) + -1w = 5(w + -1) + 16(2w + 3) (-7 * 3 + 2w * 3) + -1w = 5(w + -1) + 16(2w + 3) (-21 + 6w) + -1w = 5(w + -1) + 16(2w + 3) Combine like terms: 6w + -1w = 5w -21 + 5w = 5(w + -1) + 16(2w + 3) Reorder the terms: -21 + 5w = 5(-1 + w) + 16(2w + 3) -21 + 5w = (-1 * 5 + w * 5) + 16(2w + 3) -21 + 5w = (-5 + 5w) + 16(2w + 3) Reorder the terms: -21 + 5w = -5 + 5w + 16(3 + 2w) -21 + 5w = -5 + 5w + (3 * 16 + 2w * 16) -21 + 5w = -5 + 5w + (48 + 32w) Reorder the terms: -21 + 5w = -5 + 48 + 5w + 32w Combine like terms: -5 + 48 = 43 -21 + 5w = 43 + 5w + 32w Combine like terms: 5w + 32w = 37w -21 + 5w = 43 + 37w Solving -21 + 5w = 43 + 37w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-37w' to each side of the equation. -21 + 5w + -37w = 43 + 37w + -37w Combine like terms: 5w + -37w = -32w -21 + -32w = 43 + 37w + -37w Combine like terms: 37w + -37w = 0 -21 + -32w = 43 + 0 -21 + -32w = 43 Add '21' to each side of the equation. -21 + 21 + -32w = 43 + 21 Combine like terms: -21 + 21 = 0 0 + -32w = 43 + 21 -32w = 43 + 21 Combine like terms: 43 + 21 = 64 -32w = 64 Divide each side by '-32'. w = -2 Simplifying w = -2
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