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Simplifying 1x + -5(x + 1) = 7(6x + -1) + 2 Reorder the terms: 1x + -5(1 + x) = 7(6x + -1) + 2 1x + (1 * -5 + x * -5) = 7(6x + -1) + 2 1x + (-5 + -5x) = 7(6x + -1) + 2 Reorder the terms: -5 + 1x + -5x = 7(6x + -1) + 2 Combine like terms: 1x + -5x = -4x -5 + -4x = 7(6x + -1) + 2 Reorder the terms: -5 + -4x = 7(-1 + 6x) + 2 -5 + -4x = (-1 * 7 + 6x * 7) + 2 -5 + -4x = (-7 + 42x) + 2 Reorder the terms: -5 + -4x = -7 + 2 + 42x Combine like terms: -7 + 2 = -5 -5 + -4x = -5 + 42x Add '5' to each side of the equation. -5 + 5 + -4x = -5 + 5 + 42x Combine like terms: -5 + 5 = 0 0 + -4x = -5 + 5 + 42x -4x = -5 + 5 + 42x Combine like terms: -5 + 5 = 0 -4x = 0 + 42x -4x = 42x Solving -4x = 42x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42x' to each side of the equation. -4x + -42x = 42x + -42x Combine like terms: -4x + -42x = -46x -46x = 42x + -42x Combine like terms: 42x + -42x = 0 -46x = 0 Divide each side by '-46'. x = 0 Simplifying x = 0
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