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Simplifying 7x + 12(x + -9) = 5(3x + -2) + 8(x + -3) Reorder the terms: 7x + 12(-9 + x) = 5(3x + -2) + 8(x + -3) 7x + (-9 * 12 + x * 12) = 5(3x + -2) + 8(x + -3) 7x + (-108 + 12x) = 5(3x + -2) + 8(x + -3) Reorder the terms: -108 + 7x + 12x = 5(3x + -2) + 8(x + -3) Combine like terms: 7x + 12x = 19x -108 + 19x = 5(3x + -2) + 8(x + -3) Reorder the terms: -108 + 19x = 5(-2 + 3x) + 8(x + -3) -108 + 19x = (-2 * 5 + 3x * 5) + 8(x + -3) -108 + 19x = (-10 + 15x) + 8(x + -3) Reorder the terms: -108 + 19x = -10 + 15x + 8(-3 + x) -108 + 19x = -10 + 15x + (-3 * 8 + x * 8) -108 + 19x = -10 + 15x + (-24 + 8x) Reorder the terms: -108 + 19x = -10 + -24 + 15x + 8x Combine like terms: -10 + -24 = -34 -108 + 19x = -34 + 15x + 8x Combine like terms: 15x + 8x = 23x -108 + 19x = -34 + 23x Solving -108 + 19x = -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. -108 + 19x + -23x = -34 + 23x + -23x Combine like terms: 19x + -23x = -4x -108 + -4x = -34 + 23x + -23x Combine like terms: 23x + -23x = 0 -108 + -4x = -34 + 0 -108 + -4x = -34 Add '108' to each side of the equation. -108 + 108 + -4x = -34 + 108 Combine like terms: -108 + 108 = 0 0 + -4x = -34 + 108 -4x = -34 + 108 Combine like terms: -34 + 108 = 74 -4x = 74 Divide each side by '-4'. x = -18.5 Simplifying x = -18.5
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