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Simplifying 12 + 5w = 5(-1w + -8) + -4(6w + -2) Reorder the terms: 12 + 5w = 5(-8 + -1w) + -4(6w + -2) 12 + 5w = (-8 * 5 + -1w * 5) + -4(6w + -2) 12 + 5w = (-40 + -5w) + -4(6w + -2) Reorder the terms: 12 + 5w = -40 + -5w + -4(-2 + 6w) 12 + 5w = -40 + -5w + (-2 * -4 + 6w * -4) 12 + 5w = -40 + -5w + (8 + -24w) Reorder the terms: 12 + 5w = -40 + 8 + -5w + -24w Combine like terms: -40 + 8 = -32 12 + 5w = -32 + -5w + -24w Combine like terms: -5w + -24w = -29w 12 + 5w = -32 + -29w Solving 12 + 5w = -32 + -29w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '29w' to each side of the equation. 12 + 5w + 29w = -32 + -29w + 29w Combine like terms: 5w + 29w = 34w 12 + 34w = -32 + -29w + 29w Combine like terms: -29w + 29w = 0 12 + 34w = -32 + 0 12 + 34w = -32 Add '-12' to each side of the equation. 12 + -12 + 34w = -32 + -12 Combine like terms: 12 + -12 = 0 0 + 34w = -32 + -12 34w = -32 + -12 Combine like terms: -32 + -12 = -44 34w = -44 Divide each side by '34'. w = -1.294117647 Simplifying w = -1.294117647
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