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Simplifying 4(2x + 7) + -6(4x + -8) = 12x + 3(4x + -9) Reorder the terms: 4(7 + 2x) + -6(4x + -8) = 12x + 3(4x + -9) (7 * 4 + 2x * 4) + -6(4x + -8) = 12x + 3(4x + -9) (28 + 8x) + -6(4x + -8) = 12x + 3(4x + -9) Reorder the terms: 28 + 8x + -6(-8 + 4x) = 12x + 3(4x + -9) 28 + 8x + (-8 * -6 + 4x * -6) = 12x + 3(4x + -9) 28 + 8x + (48 + -24x) = 12x + 3(4x + -9) Reorder the terms: 28 + 48 + 8x + -24x = 12x + 3(4x + -9) Combine like terms: 28 + 48 = 76 76 + 8x + -24x = 12x + 3(4x + -9) Combine like terms: 8x + -24x = -16x 76 + -16x = 12x + 3(4x + -9) Reorder the terms: 76 + -16x = 12x + 3(-9 + 4x) 76 + -16x = 12x + (-9 * 3 + 4x * 3) 76 + -16x = 12x + (-27 + 12x) Reorder the terms: 76 + -16x = -27 + 12x + 12x Combine like terms: 12x + 12x = 24x 76 + -16x = -27 + 24x Solving 76 + -16x = -27 + 24x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24x' to each side of the equation. 76 + -16x + -24x = -27 + 24x + -24x Combine like terms: -16x + -24x = -40x 76 + -40x = -27 + 24x + -24x Combine like terms: 24x + -24x = 0 76 + -40x = -27 + 0 76 + -40x = -27 Add '-76' to each side of the equation. 76 + -76 + -40x = -27 + -76 Combine like terms: 76 + -76 = 0 0 + -40x = -27 + -76 -40x = -27 + -76 Combine like terms: -27 + -76 = -103 -40x = -103 Divide each side by '-40'. x = 2.575 Simplifying x = 2.575
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