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Simplifying 0.5(5x + 3) + 8.2(2x + -1) = 2.2(10x + 4) Reorder the terms: 0.5(3 + 5x) + 8.2(2x + -1) = 2.2(10x + 4) (3 * 0.5 + 5x * 0.5) + 8.2(2x + -1) = 2.2(10x + 4) (1.5 + 2.5x) + 8.2(2x + -1) = 2.2(10x + 4) Reorder the terms: 1.5 + 2.5x + 8.2(-1 + 2x) = 2.2(10x + 4) 1.5 + 2.5x + (-1 * 8.2 + 2x * 8.2) = 2.2(10x + 4) 1.5 + 2.5x + (-8.2 + 16.4x) = 2.2(10x + 4) Reorder the terms: 1.5 + -8.2 + 2.5x + 16.4x = 2.2(10x + 4) Combine like terms: 1.5 + -8.2 = -6.7 -6.7 + 2.5x + 16.4x = 2.2(10x + 4) Combine like terms: 2.5x + 16.4x = 18.9x -6.7 + 18.9x = 2.2(10x + 4) Reorder the terms: -6.7 + 18.9x = 2.2(4 + 10x) -6.7 + 18.9x = (4 * 2.2 + 10x * 2.2) -6.7 + 18.9x = (8.8 + 22x) Solving -6.7 + 18.9x = 8.8 + 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. -6.7 + 18.9x + -22x = 8.8 + 22x + -22x Combine like terms: 18.9x + -22x = -3.1x -6.7 + -3.1x = 8.8 + 22x + -22x Combine like terms: 22x + -22x = 0 -6.7 + -3.1x = 8.8 + 0 -6.7 + -3.1x = 8.8 Add '6.7' to each side of the equation. -6.7 + 6.7 + -3.1x = 8.8 + 6.7 Combine like terms: -6.7 + 6.7 = 0.0 0.0 + -3.1x = 8.8 + 6.7 -3.1x = 8.8 + 6.7 Combine like terms: 8.8 + 6.7 = 15.5 -3.1x = 15.5 Divide each side by '-3.1'. x = -5 Simplifying x = -5
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