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Simplifying 2(3x + 2) + -5(x + 3) = 6 + -8(x + 1) Reorder the terms: 2(2 + 3x) + -5(x + 3) = 6 + -8(x + 1) (2 * 2 + 3x * 2) + -5(x + 3) = 6 + -8(x + 1) (4 + 6x) + -5(x + 3) = 6 + -8(x + 1) Reorder the terms: 4 + 6x + -5(3 + x) = 6 + -8(x + 1) 4 + 6x + (3 * -5 + x * -5) = 6 + -8(x + 1) 4 + 6x + (-15 + -5x) = 6 + -8(x + 1) Reorder the terms: 4 + -15 + 6x + -5x = 6 + -8(x + 1) Combine like terms: 4 + -15 = -11 -11 + 6x + -5x = 6 + -8(x + 1) Combine like terms: 6x + -5x = 1x -11 + 1x = 6 + -8(x + 1) Reorder the terms: -11 + 1x = 6 + -8(1 + x) -11 + 1x = 6 + (1 * -8 + x * -8) -11 + 1x = 6 + (-8 + -8x) Combine like terms: 6 + -8 = -2 -11 + 1x = -2 + -8x Solving -11 + 1x = -2 + -8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8x' to each side of the equation. -11 + 1x + 8x = -2 + -8x + 8x Combine like terms: 1x + 8x = 9x -11 + 9x = -2 + -8x + 8x Combine like terms: -8x + 8x = 0 -11 + 9x = -2 + 0 -11 + 9x = -2 Add '11' to each side of the equation. -11 + 11 + 9x = -2 + 11 Combine like terms: -11 + 11 = 0 0 + 9x = -2 + 11 9x = -2 + 11 Combine like terms: -2 + 11 = 9 9x = 9 Divide each side by '9'. x = 1 Simplifying x = 1
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