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Simplifying 3(2x + 1) + 7(6x + -1) = 5(12x + -7) + 23 Reorder the terms: 3(1 + 2x) + 7(6x + -1) = 5(12x + -7) + 23 (1 * 3 + 2x * 3) + 7(6x + -1) = 5(12x + -7) + 23 (3 + 6x) + 7(6x + -1) = 5(12x + -7) + 23 Reorder the terms: 3 + 6x + 7(-1 + 6x) = 5(12x + -7) + 23 3 + 6x + (-1 * 7 + 6x * 7) = 5(12x + -7) + 23 3 + 6x + (-7 + 42x) = 5(12x + -7) + 23 Reorder the terms: 3 + -7 + 6x + 42x = 5(12x + -7) + 23 Combine like terms: 3 + -7 = -4 -4 + 6x + 42x = 5(12x + -7) + 23 Combine like terms: 6x + 42x = 48x -4 + 48x = 5(12x + -7) + 23 Reorder the terms: -4 + 48x = 5(-7 + 12x) + 23 -4 + 48x = (-7 * 5 + 12x * 5) + 23 -4 + 48x = (-35 + 60x) + 23 Reorder the terms: -4 + 48x = -35 + 23 + 60x Combine like terms: -35 + 23 = -12 -4 + 48x = -12 + 60x Solving -4 + 48x = -12 + 60x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60x' to each side of the equation. -4 + 48x + -60x = -12 + 60x + -60x Combine like terms: 48x + -60x = -12x -4 + -12x = -12 + 60x + -60x Combine like terms: 60x + -60x = 0 -4 + -12x = -12 + 0 -4 + -12x = -12 Add '4' to each side of the equation. -4 + 4 + -12x = -12 + 4 Combine like terms: -4 + 4 = 0 0 + -12x = -12 + 4 -12x = -12 + 4 Combine like terms: -12 + 4 = -8 -12x = -8 Divide each side by '-12'. x = 0.6666666667 Simplifying x = 0.6666666667
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