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Simplifying 4x + 2(x + 2) + -3(x + 1) = 52 Reorder the terms: 4x + 2(2 + x) + -3(x + 1) = 52 4x + (2 * 2 + x * 2) + -3(x + 1) = 52 4x + (4 + 2x) + -3(x + 1) = 52 Reorder the terms: 4x + 4 + 2x + -3(1 + x) = 52 4x + 4 + 2x + (1 * -3 + x * -3) = 52 4x + 4 + 2x + (-3 + -3x) = 52 Reorder the terms: 4 + -3 + 4x + 2x + -3x = 52 Combine like terms: 4 + -3 = 1 1 + 4x + 2x + -3x = 52 Combine like terms: 4x + 2x = 6x 1 + 6x + -3x = 52 Combine like terms: 6x + -3x = 3x 1 + 3x = 52 Solving 1 + 3x = 52 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 52 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 52 + -1 3x = 52 + -1 Combine like terms: 52 + -1 = 51 3x = 51 Divide each side by '3'. x = 17 Simplifying x = 17
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