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Simplifying 5(3x + -2) + 1 + -3(2x + 1) = 2(x + 1) Reorder the terms: 5(-2 + 3x) + 1 + -3(2x + 1) = 2(x + 1) (-2 * 5 + 3x * 5) + 1 + -3(2x + 1) = 2(x + 1) (-10 + 15x) + 1 + -3(2x + 1) = 2(x + 1) Reorder the terms: -10 + 15x + 1 + -3(1 + 2x) = 2(x + 1) -10 + 15x + 1 + (1 * -3 + 2x * -3) = 2(x + 1) -10 + 15x + 1 + (-3 + -6x) = 2(x + 1) Reorder the terms: -10 + 1 + -3 + 15x + -6x = 2(x + 1) Combine like terms: -10 + 1 = -9 -9 + -3 + 15x + -6x = 2(x + 1) Combine like terms: -9 + -3 = -12 -12 + 15x + -6x = 2(x + 1) Combine like terms: 15x + -6x = 9x -12 + 9x = 2(x + 1) Reorder the terms: -12 + 9x = 2(1 + x) -12 + 9x = (1 * 2 + x * 2) -12 + 9x = (2 + 2x) Solving -12 + 9x = 2 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -12 + 9x + -2x = 2 + 2x + -2x Combine like terms: 9x + -2x = 7x -12 + 7x = 2 + 2x + -2x Combine like terms: 2x + -2x = 0 -12 + 7x = 2 + 0 -12 + 7x = 2 Add '12' to each side of the equation. -12 + 12 + 7x = 2 + 12 Combine like terms: -12 + 12 = 0 0 + 7x = 2 + 12 7x = 2 + 12 Combine like terms: 2 + 12 = 14 7x = 14 Divide each side by '7'. x = 2 Simplifying x = 2
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