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Simplifying 6(x + 3) + -7(x + 5) = 4(x + 1) + -2(x + 6) + 12 Reorder the terms: 6(3 + x) + -7(x + 5) = 4(x + 1) + -2(x + 6) + 12 (3 * 6 + x * 6) + -7(x + 5) = 4(x + 1) + -2(x + 6) + 12 (18 + 6x) + -7(x + 5) = 4(x + 1) + -2(x + 6) + 12 Reorder the terms: 18 + 6x + -7(5 + x) = 4(x + 1) + -2(x + 6) + 12 18 + 6x + (5 * -7 + x * -7) = 4(x + 1) + -2(x + 6) + 12 18 + 6x + (-35 + -7x) = 4(x + 1) + -2(x + 6) + 12 Reorder the terms: 18 + -35 + 6x + -7x = 4(x + 1) + -2(x + 6) + 12 Combine like terms: 18 + -35 = -17 -17 + 6x + -7x = 4(x + 1) + -2(x + 6) + 12 Combine like terms: 6x + -7x = -1x -17 + -1x = 4(x + 1) + -2(x + 6) + 12 Reorder the terms: -17 + -1x = 4(1 + x) + -2(x + 6) + 12 -17 + -1x = (1 * 4 + x * 4) + -2(x + 6) + 12 -17 + -1x = (4 + 4x) + -2(x + 6) + 12 Reorder the terms: -17 + -1x = 4 + 4x + -2(6 + x) + 12 -17 + -1x = 4 + 4x + (6 * -2 + x * -2) + 12 -17 + -1x = 4 + 4x + (-12 + -2x) + 12 Reorder the terms: -17 + -1x = 4 + -12 + 12 + 4x + -2x Combine like terms: 4 + -12 = -8 -17 + -1x = -8 + 12 + 4x + -2x Combine like terms: -8 + 12 = 4 -17 + -1x = 4 + 4x + -2x Combine like terms: 4x + -2x = 2x -17 + -1x = 4 + 2x Solving -17 + -1x = 4 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -17 + -1x + -2x = 4 + 2x + -2x Combine like terms: -1x + -2x = -3x -17 + -3x = 4 + 2x + -2x Combine like terms: 2x + -2x = 0 -17 + -3x = 4 + 0 -17 + -3x = 4 Add '17' to each side of the equation. -17 + 17 + -3x = 4 + 17 Combine like terms: -17 + 17 = 0 0 + -3x = 4 + 17 -3x = 4 + 17 Combine like terms: 4 + 17 = 21 -3x = 21 Divide each side by '-3'. x = -7 Simplifying x = -7
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