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Simplifying 0.5(4x + -5) + 1.5(2x + 1) = x + 3 Reorder the terms: 0.5(-5 + 4x) + 1.5(2x + 1) = x + 3 (-5 * 0.5 + 4x * 0.5) + 1.5(2x + 1) = x + 3 (-2.5 + 2x) + 1.5(2x + 1) = x + 3 Reorder the terms: -2.5 + 2x + 1.5(1 + 2x) = x + 3 -2.5 + 2x + (1 * 1.5 + 2x * 1.5) = x + 3 -2.5 + 2x + (1.5 + 3x) = x + 3 Reorder the terms: -2.5 + 1.5 + 2x + 3x = x + 3 Combine like terms: -2.5 + 1.5 = -1 -1 + 2x + 3x = x + 3 Combine like terms: 2x + 3x = 5x -1 + 5x = x + 3 Reorder the terms: -1 + 5x = 3 + x Solving -1 + 5x = 3 + x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. -1 + 5x + -1x = 3 + x + -1x Combine like terms: 5x + -1x = 4x -1 + 4x = 3 + x + -1x Combine like terms: x + -1x = 0 -1 + 4x = 3 + 0 -1 + 4x = 3 Add '1' to each side of the equation. -1 + 1 + 4x = 3 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 3 + 1 4x = 3 + 1 Combine like terms: 3 + 1 = 4 4x = 4 Divide each side by '4'. x = 1 Simplifying x = 1
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