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Simplifying 7x + 12(x + -9) + 4(3x + 6) = 5(3x + -2) + 8(x + -3) Reorder the terms: 7x + 12(-9 + x) + 4(3x + 6) = 5(3x + -2) + 8(x + -3) 7x + (-9 * 12 + x * 12) + 4(3x + 6) = 5(3x + -2) + 8(x + -3) 7x + (-108 + 12x) + 4(3x + 6) = 5(3x + -2) + 8(x + -3) Reorder the terms: 7x + -108 + 12x + 4(6 + 3x) = 5(3x + -2) + 8(x + -3) 7x + -108 + 12x + (6 * 4 + 3x * 4) = 5(3x + -2) + 8(x + -3) 7x + -108 + 12x + (24 + 12x) = 5(3x + -2) + 8(x + -3) Reorder the terms: -108 + 24 + 7x + 12x + 12x = 5(3x + -2) + 8(x + -3) Combine like terms: -108 + 24 = -84 -84 + 7x + 12x + 12x = 5(3x + -2) + 8(x + -3) Combine like terms: 7x + 12x = 19x -84 + 19x + 12x = 5(3x + -2) + 8(x + -3) Combine like terms: 19x + 12x = 31x -84 + 31x = 5(3x + -2) + 8(x + -3) Reorder the terms: -84 + 31x = 5(-2 + 3x) + 8(x + -3) -84 + 31x = (-2 * 5 + 3x * 5) + 8(x + -3) -84 + 31x = (-10 + 15x) + 8(x + -3) Reorder the terms: -84 + 31x = -10 + 15x + 8(-3 + x) -84 + 31x = -10 + 15x + (-3 * 8 + x * 8) -84 + 31x = -10 + 15x + (-24 + 8x) Reorder the terms: -84 + 31x = -10 + -24 + 15x + 8x Combine like terms: -10 + -24 = -34 -84 + 31x = -34 + 15x + 8x Combine like terms: 15x + 8x = 23x -84 + 31x = -34 + 23x Solving -84 + 31x = -34 + 23x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23x' to each side of the equation. -84 + 31x + -23x = -34 + 23x + -23x Combine like terms: 31x + -23x = 8x -84 + 8x = -34 + 23x + -23x Combine like terms: 23x + -23x = 0 -84 + 8x = -34 + 0 -84 + 8x = -34 Add '84' to each side of the equation. -84 + 84 + 8x = -34 + 84 Combine like terms: -84 + 84 = 0 0 + 8x = -34 + 84 8x = -34 + 84 Combine like terms: -34 + 84 = 50 8x = 50 Divide each side by '8'. x = 6.25 Simplifying x = 6.25
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