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Simplifying 4(x + -2) + -5(2x + -6) = 8(x + 1) + -3(2x + 3) Reorder the terms: 4(-2 + x) + -5(2x + -6) = 8(x + 1) + -3(2x + 3) (-2 * 4 + x * 4) + -5(2x + -6) = 8(x + 1) + -3(2x + 3) (-8 + 4x) + -5(2x + -6) = 8(x + 1) + -3(2x + 3) Reorder the terms: -8 + 4x + -5(-6 + 2x) = 8(x + 1) + -3(2x + 3) -8 + 4x + (-6 * -5 + 2x * -5) = 8(x + 1) + -3(2x + 3) -8 + 4x + (30 + -10x) = 8(x + 1) + -3(2x + 3) Reorder the terms: -8 + 30 + 4x + -10x = 8(x + 1) + -3(2x + 3) Combine like terms: -8 + 30 = 22 22 + 4x + -10x = 8(x + 1) + -3(2x + 3) Combine like terms: 4x + -10x = -6x 22 + -6x = 8(x + 1) + -3(2x + 3) Reorder the terms: 22 + -6x = 8(1 + x) + -3(2x + 3) 22 + -6x = (1 * 8 + x * 8) + -3(2x + 3) 22 + -6x = (8 + 8x) + -3(2x + 3) Reorder the terms: 22 + -6x = 8 + 8x + -3(3 + 2x) 22 + -6x = 8 + 8x + (3 * -3 + 2x * -3) 22 + -6x = 8 + 8x + (-9 + -6x) Reorder the terms: 22 + -6x = 8 + -9 + 8x + -6x Combine like terms: 8 + -9 = -1 22 + -6x = -1 + 8x + -6x Combine like terms: 8x + -6x = 2x 22 + -6x = -1 + 2x Solving 22 + -6x = -1 + 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. 22 + -6x + -2x = -1 + 2x + -2x Combine like terms: -6x + -2x = -8x 22 + -8x = -1 + 2x + -2x Combine like terms: 2x + -2x = 0 22 + -8x = -1 + 0 22 + -8x = -1 Add '-22' to each side of the equation. 22 + -22 + -8x = -1 + -22 Combine like terms: 22 + -22 = 0 0 + -8x = -1 + -22 -8x = -1 + -22 Combine like terms: -1 + -22 = -23 -8x = -23 Divide each side by '-8'. x = 2.875 Simplifying x = 2.875
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