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Simplifying 3(2x + -1) + 4(x + 3) = 5(2x + -1) + 4(3x + -1) Reorder the terms: 3(-1 + 2x) + 4(x + 3) = 5(2x + -1) + 4(3x + -1) (-1 * 3 + 2x * 3) + 4(x + 3) = 5(2x + -1) + 4(3x + -1) (-3 + 6x) + 4(x + 3) = 5(2x + -1) + 4(3x + -1) Reorder the terms: -3 + 6x + 4(3 + x) = 5(2x + -1) + 4(3x + -1) -3 + 6x + (3 * 4 + x * 4) = 5(2x + -1) + 4(3x + -1) -3 + 6x + (12 + 4x) = 5(2x + -1) + 4(3x + -1) Reorder the terms: -3 + 12 + 6x + 4x = 5(2x + -1) + 4(3x + -1) Combine like terms: -3 + 12 = 9 9 + 6x + 4x = 5(2x + -1) + 4(3x + -1) Combine like terms: 6x + 4x = 10x 9 + 10x = 5(2x + -1) + 4(3x + -1) Reorder the terms: 9 + 10x = 5(-1 + 2x) + 4(3x + -1) 9 + 10x = (-1 * 5 + 2x * 5) + 4(3x + -1) 9 + 10x = (-5 + 10x) + 4(3x + -1) Reorder the terms: 9 + 10x = -5 + 10x + 4(-1 + 3x) 9 + 10x = -5 + 10x + (-1 * 4 + 3x * 4) 9 + 10x = -5 + 10x + (-4 + 12x) Reorder the terms: 9 + 10x = -5 + -4 + 10x + 12x Combine like terms: -5 + -4 = -9 9 + 10x = -9 + 10x + 12x Combine like terms: 10x + 12x = 22x 9 + 10x = -9 + 22x Solving 9 + 10x = -9 + 22x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22x' to each side of the equation. 9 + 10x + -22x = -9 + 22x + -22x Combine like terms: 10x + -22x = -12x 9 + -12x = -9 + 22x + -22x Combine like terms: 22x + -22x = 0 9 + -12x = -9 + 0 9 + -12x = -9 Add '-9' to each side of the equation. 9 + -9 + -12x = -9 + -9 Combine like terms: 9 + -9 = 0 0 + -12x = -9 + -9 -12x = -9 + -9 Combine like terms: -9 + -9 = -18 -12x = -18 Divide each side by '-12'. x = 1.5 Simplifying x = 1.5
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