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Simplifying 3(2x + -1) + 2(3x + -1) = 51 + -5(x + 1) Reorder the terms: 3(-1 + 2x) + 2(3x + -1) = 51 + -5(x + 1) (-1 * 3 + 2x * 3) + 2(3x + -1) = 51 + -5(x + 1) (-3 + 6x) + 2(3x + -1) = 51 + -5(x + 1) Reorder the terms: -3 + 6x + 2(-1 + 3x) = 51 + -5(x + 1) -3 + 6x + (-1 * 2 + 3x * 2) = 51 + -5(x + 1) -3 + 6x + (-2 + 6x) = 51 + -5(x + 1) Reorder the terms: -3 + -2 + 6x + 6x = 51 + -5(x + 1) Combine like terms: -3 + -2 = -5 -5 + 6x + 6x = 51 + -5(x + 1) Combine like terms: 6x + 6x = 12x -5 + 12x = 51 + -5(x + 1) Reorder the terms: -5 + 12x = 51 + -5(1 + x) -5 + 12x = 51 + (1 * -5 + x * -5) -5 + 12x = 51 + (-5 + -5x) Combine like terms: 51 + -5 = 46 -5 + 12x = 46 + -5x Solving -5 + 12x = 46 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -5 + 12x + 5x = 46 + -5x + 5x Combine like terms: 12x + 5x = 17x -5 + 17x = 46 + -5x + 5x Combine like terms: -5x + 5x = 0 -5 + 17x = 46 + 0 -5 + 17x = 46 Add '5' to each side of the equation. -5 + 5 + 17x = 46 + 5 Combine like terms: -5 + 5 = 0 0 + 17x = 46 + 5 17x = 46 + 5 Combine like terms: 46 + 5 = 51 17x = 51 Divide each side by '17'. x = 3 Simplifying x = 3
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