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Simplifying 4(1 + x) + -5(x + 2) = 102 (1 * 4 + x * 4) + -5(x + 2) = 102 (4 + 4x) + -5(x + 2) = 102 Reorder the terms: 4 + 4x + -5(2 + x) = 102 4 + 4x + (2 * -5 + x * -5) = 102 4 + 4x + (-10 + -5x) = 102 Reorder the terms: 4 + -10 + 4x + -5x = 102 Combine like terms: 4 + -10 = -6 -6 + 4x + -5x = 102 Combine like terms: 4x + -5x = -1x -6 + -1x = 102 Solving -6 + -1x = 102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 102 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 102 + 6 -1x = 102 + 6 Combine like terms: 102 + 6 = 108 -1x = 108 Divide each side by '-1'. x = -108 Simplifying x = -108
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