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Simplifying 5(2 + w) = 3(2w + -1) + -2(4 + -3w) (2 * 5 + w * 5) = 3(2w + -1) + -2(4 + -3w) (10 + 5w) = 3(2w + -1) + -2(4 + -3w) Reorder the terms: 10 + 5w = 3(-1 + 2w) + -2(4 + -3w) 10 + 5w = (-1 * 3 + 2w * 3) + -2(4 + -3w) 10 + 5w = (-3 + 6w) + -2(4 + -3w) 10 + 5w = -3 + 6w + (4 * -2 + -3w * -2) 10 + 5w = -3 + 6w + (-8 + 6w) Reorder the terms: 10 + 5w = -3 + -8 + 6w + 6w Combine like terms: -3 + -8 = -11 10 + 5w = -11 + 6w + 6w Combine like terms: 6w + 6w = 12w 10 + 5w = -11 + 12w Solving 10 + 5w = -11 + 12w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12w' to each side of the equation. 10 + 5w + -12w = -11 + 12w + -12w Combine like terms: 5w + -12w = -7w 10 + -7w = -11 + 12w + -12w Combine like terms: 12w + -12w = 0 10 + -7w = -11 + 0 10 + -7w = -11 Add '-10' to each side of the equation. 10 + -10 + -7w = -11 + -10 Combine like terms: 10 + -10 = 0 0 + -7w = -11 + -10 -7w = -11 + -10 Combine like terms: -11 + -10 = -21 -7w = -21 Divide each side by '-7'. w = 3 Simplifying w = 3
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