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Simplifying 12(x + 1) = 7(x + 6) Reorder the terms: 12(1 + x) = 7(x + 6) (1 * 12 + x * 12) = 7(x + 6) (12 + 12x) = 7(x + 6) Reorder the terms: 12 + 12x = 7(6 + x) 12 + 12x = (6 * 7 + x * 7) 12 + 12x = (42 + 7x) Solving 12 + 12x = 42 + 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. 12 + 12x + -7x = 42 + 7x + -7x Combine like terms: 12x + -7x = 5x 12 + 5x = 42 + 7x + -7x Combine like terms: 7x + -7x = 0 12 + 5x = 42 + 0 12 + 5x = 42 Add '-12' to each side of the equation. 12 + -12 + 5x = 42 + -12 Combine like terms: 12 + -12 = 0 0 + 5x = 42 + -12 5x = 42 + -12 Combine like terms: 42 + -12 = 30 5x = 30 Divide each side by '5'. x = 6 Simplifying x = 6
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