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Simplifying 5(7 + -5w) + 12 = -178 (7 * 5 + -5w * 5) + 12 = -178 (35 + -25w) + 12 = -178 Reorder the terms: 35 + 12 + -25w = -178 Combine like terms: 35 + 12 = 47 47 + -25w = -178 Solving 47 + -25w = -178 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-47' to each side of the equation. 47 + -47 + -25w = -178 + -47 Combine like terms: 47 + -47 = 0 0 + -25w = -178 + -47 -25w = -178 + -47 Combine like terms: -178 + -47 = -225 -25w = -225 Divide each side by '-25'. w = 9 Simplifying w = 9
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