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Simplifying 9(2x + 6) + 4(3x + 5) = 10(5x + 1) + 6(2x + 3) Reorder the terms: 9(6 + 2x) + 4(3x + 5) = 10(5x + 1) + 6(2x + 3) (6 * 9 + 2x * 9) + 4(3x + 5) = 10(5x + 1) + 6(2x + 3) (54 + 18x) + 4(3x + 5) = 10(5x + 1) + 6(2x + 3) Reorder the terms: 54 + 18x + 4(5 + 3x) = 10(5x + 1) + 6(2x + 3) 54 + 18x + (5 * 4 + 3x * 4) = 10(5x + 1) + 6(2x + 3) 54 + 18x + (20 + 12x) = 10(5x + 1) + 6(2x + 3) Reorder the terms: 54 + 20 + 18x + 12x = 10(5x + 1) + 6(2x + 3) Combine like terms: 54 + 20 = 74 74 + 18x + 12x = 10(5x + 1) + 6(2x + 3) Combine like terms: 18x + 12x = 30x 74 + 30x = 10(5x + 1) + 6(2x + 3) Reorder the terms: 74 + 30x = 10(1 + 5x) + 6(2x + 3) 74 + 30x = (1 * 10 + 5x * 10) + 6(2x + 3) 74 + 30x = (10 + 50x) + 6(2x + 3) Reorder the terms: 74 + 30x = 10 + 50x + 6(3 + 2x) 74 + 30x = 10 + 50x + (3 * 6 + 2x * 6) 74 + 30x = 10 + 50x + (18 + 12x) Reorder the terms: 74 + 30x = 10 + 18 + 50x + 12x Combine like terms: 10 + 18 = 28 74 + 30x = 28 + 50x + 12x Combine like terms: 50x + 12x = 62x 74 + 30x = 28 + 62x Solving 74 + 30x = 28 + 62x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62x' to each side of the equation. 74 + 30x + -62x = 28 + 62x + -62x Combine like terms: 30x + -62x = -32x 74 + -32x = 28 + 62x + -62x Combine like terms: 62x + -62x = 0 74 + -32x = 28 + 0 74 + -32x = 28 Add '-74' to each side of the equation. 74 + -74 + -32x = 28 + -74 Combine like terms: 74 + -74 = 0 0 + -32x = 28 + -74 -32x = 28 + -74 Combine like terms: 28 + -74 = -46 -32x = -46 Divide each side by '-32'. x = 1.4375 Simplifying x = 1.4375
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