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Simplifying 12(3x + -5) + -6(5x + 1) = 3(2x + 6) + -4(3x + -12) + -24 Reorder the terms: 12(-5 + 3x) + -6(5x + 1) = 3(2x + 6) + -4(3x + -12) + -24 (-5 * 12 + 3x * 12) + -6(5x + 1) = 3(2x + 6) + -4(3x + -12) + -24 (-60 + 36x) + -6(5x + 1) = 3(2x + 6) + -4(3x + -12) + -24 Reorder the terms: -60 + 36x + -6(1 + 5x) = 3(2x + 6) + -4(3x + -12) + -24 -60 + 36x + (1 * -6 + 5x * -6) = 3(2x + 6) + -4(3x + -12) + -24 -60 + 36x + (-6 + -30x) = 3(2x + 6) + -4(3x + -12) + -24 Reorder the terms: -60 + -6 + 36x + -30x = 3(2x + 6) + -4(3x + -12) + -24 Combine like terms: -60 + -6 = -66 -66 + 36x + -30x = 3(2x + 6) + -4(3x + -12) + -24 Combine like terms: 36x + -30x = 6x -66 + 6x = 3(2x + 6) + -4(3x + -12) + -24 Reorder the terms: -66 + 6x = 3(6 + 2x) + -4(3x + -12) + -24 -66 + 6x = (6 * 3 + 2x * 3) + -4(3x + -12) + -24 -66 + 6x = (18 + 6x) + -4(3x + -12) + -24 Reorder the terms: -66 + 6x = 18 + 6x + -4(-12 + 3x) + -24 -66 + 6x = 18 + 6x + (-12 * -4 + 3x * -4) + -24 -66 + 6x = 18 + 6x + (48 + -12x) + -24 Reorder the terms: -66 + 6x = 18 + 48 + -24 + 6x + -12x Combine like terms: 18 + 48 = 66 -66 + 6x = 66 + -24 + 6x + -12x Combine like terms: 66 + -24 = 42 -66 + 6x = 42 + 6x + -12x Combine like terms: 6x + -12x = -6x -66 + 6x = 42 + -6x Solving -66 + 6x = 42 + -6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6x' to each side of the equation. -66 + 6x + 6x = 42 + -6x + 6x Combine like terms: 6x + 6x = 12x -66 + 12x = 42 + -6x + 6x Combine like terms: -6x + 6x = 0 -66 + 12x = 42 + 0 -66 + 12x = 42 Add '66' to each side of the equation. -66 + 66 + 12x = 42 + 66 Combine like terms: -66 + 66 = 0 0 + 12x = 42 + 66 12x = 42 + 66 Combine like terms: 42 + 66 = 108 12x = 108 Divide each side by '12'. x = 9 Simplifying x = 9
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