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Simplifying 2(2x + 2) + 0.5(x + 1) = 4(x + 2) Reorder the terms: 2(2 + 2x) + 0.5(x + 1) = 4(x + 2) (2 * 2 + 2x * 2) + 0.5(x + 1) = 4(x + 2) (4 + 4x) + 0.5(x + 1) = 4(x + 2) Reorder the terms: 4 + 4x + 0.5(1 + x) = 4(x + 2) 4 + 4x + (1 * 0.5 + x * 0.5) = 4(x + 2) 4 + 4x + (0.5 + 0.5x) = 4(x + 2) Reorder the terms: 4 + 0.5 + 4x + 0.5x = 4(x + 2) Combine like terms: 4 + 0.5 = 4.5 4.5 + 4x + 0.5x = 4(x + 2) Combine like terms: 4x + 0.5x = 4.5x 4.5 + 4.5x = 4(x + 2) Reorder the terms: 4.5 + 4.5x = 4(2 + x) 4.5 + 4.5x = (2 * 4 + x * 4) 4.5 + 4.5x = (8 + 4x) Solving 4.5 + 4.5x = 8 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 4.5 + 4.5x + -4x = 8 + 4x + -4x Combine like terms: 4.5x + -4x = 0.5x 4.5 + 0.5x = 8 + 4x + -4x Combine like terms: 4x + -4x = 0 4.5 + 0.5x = 8 + 0 4.5 + 0.5x = 8 Add '-4.5' to each side of the equation. 4.5 + -4.5 + 0.5x = 8 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 0.5x = 8 + -4.5 0.5x = 8 + -4.5 Combine like terms: 8 + -4.5 = 3.5 0.5x = 3.5 Divide each side by '0.5'. x = 7 Simplifying x = 7
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