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Simplifying 4(3x + 7) + -6(4x + -5) = 10x + 3(2x + -7) Reorder the terms: 4(7 + 3x) + -6(4x + -5) = 10x + 3(2x + -7) (7 * 4 + 3x * 4) + -6(4x + -5) = 10x + 3(2x + -7) (28 + 12x) + -6(4x + -5) = 10x + 3(2x + -7) Reorder the terms: 28 + 12x + -6(-5 + 4x) = 10x + 3(2x + -7) 28 + 12x + (-5 * -6 + 4x * -6) = 10x + 3(2x + -7) 28 + 12x + (30 + -24x) = 10x + 3(2x + -7) Reorder the terms: 28 + 30 + 12x + -24x = 10x + 3(2x + -7) Combine like terms: 28 + 30 = 58 58 + 12x + -24x = 10x + 3(2x + -7) Combine like terms: 12x + -24x = -12x 58 + -12x = 10x + 3(2x + -7) Reorder the terms: 58 + -12x = 10x + 3(-7 + 2x) 58 + -12x = 10x + (-7 * 3 + 2x * 3) 58 + -12x = 10x + (-21 + 6x) Reorder the terms: 58 + -12x = -21 + 10x + 6x Combine like terms: 10x + 6x = 16x 58 + -12x = -21 + 16x Solving 58 + -12x = -21 + 16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16x' to each side of the equation. 58 + -12x + -16x = -21 + 16x + -16x Combine like terms: -12x + -16x = -28x 58 + -28x = -21 + 16x + -16x Combine like terms: 16x + -16x = 0 58 + -28x = -21 + 0 58 + -28x = -21 Add '-58' to each side of the equation. 58 + -58 + -28x = -21 + -58 Combine like terms: 58 + -58 = 0 0 + -28x = -21 + -58 -28x = -21 + -58 Combine like terms: -21 + -58 = -79 -28x = -79 Divide each side by '-28'. x = 2.821428571 Simplifying x = 2.821428571
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