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Simplifying 5(x + 1) + 6(x + 2) = 7(x + 3) Reorder the terms: 5(1 + x) + 6(x + 2) = 7(x + 3) (1 * 5 + x * 5) + 6(x + 2) = 7(x + 3) (5 + 5x) + 6(x + 2) = 7(x + 3) Reorder the terms: 5 + 5x + 6(2 + x) = 7(x + 3) 5 + 5x + (2 * 6 + x * 6) = 7(x + 3) 5 + 5x + (12 + 6x) = 7(x + 3) Reorder the terms: 5 + 12 + 5x + 6x = 7(x + 3) Combine like terms: 5 + 12 = 17 17 + 5x + 6x = 7(x + 3) Combine like terms: 5x + 6x = 11x 17 + 11x = 7(x + 3) Reorder the terms: 17 + 11x = 7(3 + x) 17 + 11x = (3 * 7 + x * 7) 17 + 11x = (21 + 7x) Solving 17 + 11x = 21 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 17 + 11x + -7x = 21 + 7x + -7x Combine like terms: 11x + -7x = 4x 17 + 4x = 21 + 7x + -7x Combine like terms: 7x + -7x = 0 17 + 4x = 21 + 0 17 + 4x = 21 Add '-17' to each side of the equation. 17 + -17 + 4x = 21 + -17 Combine like terms: 17 + -17 = 0 0 + 4x = 21 + -17 4x = 21 + -17 Combine like terms: 21 + -17 = 4 4x = 4 Divide each side by '4'. x = 1 Simplifying x = 1
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