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Simplifying 4(3x + 6) + -6(4x + -5) = 12x + 3(4x + -8) Reorder the terms: 4(6 + 3x) + -6(4x + -5) = 12x + 3(4x + -8) (6 * 4 + 3x * 4) + -6(4x + -5) = 12x + 3(4x + -8) (24 + 12x) + -6(4x + -5) = 12x + 3(4x + -8) Reorder the terms: 24 + 12x + -6(-5 + 4x) = 12x + 3(4x + -8) 24 + 12x + (-5 * -6 + 4x * -6) = 12x + 3(4x + -8) 24 + 12x + (30 + -24x) = 12x + 3(4x + -8) Reorder the terms: 24 + 30 + 12x + -24x = 12x + 3(4x + -8) Combine like terms: 24 + 30 = 54 54 + 12x + -24x = 12x + 3(4x + -8) Combine like terms: 12x + -24x = -12x 54 + -12x = 12x + 3(4x + -8) Reorder the terms: 54 + -12x = 12x + 3(-8 + 4x) 54 + -12x = 12x + (-8 * 3 + 4x * 3) 54 + -12x = 12x + (-24 + 12x) Reorder the terms: 54 + -12x = -24 + 12x + 12x Combine like terms: 12x + 12x = 24x 54 + -12x = -24 + 24x Solving 54 + -12x = -24 + 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. 54 + -12x + -24x = -24 + 24x + -24x Combine like terms: -12x + -24x = -36x 54 + -36x = -24 + 24x + -24x Combine like terms: 24x + -24x = 0 54 + -36x = -24 + 0 54 + -36x = -24 Add '-54' to each side of the equation. 54 + -54 + -36x = -24 + -54 Combine like terms: 54 + -54 = 0 0 + -36x = -24 + -54 -36x = -24 + -54 Combine like terms: -24 + -54 = -78 -36x = -78 Divide each side by '-36'. x = 2.166666667 Simplifying x = 2.166666667
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