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Simplifying 0.4(2x + 0.5) = 3[0.2x + (-2)] + -4 Reorder the terms: 0.4(0.5 + 2x) = 3[0.2x + (-2)] + -4 (0.5 * 0.4 + 2x * 0.4) = 3[0.2x + (-2)] + -4 (0.2 + 0.8x) = 3[0.2x + (-2)] + -4 0.2 + 0.8x = 3[0.2x + -2] + -4 Reorder the terms: 0.2 + 0.8x = 3[-2 + 0.2x] + -4 0.2 + 0.8x = [-2 * 3 + 0.2x * 3] + -4 0.2 + 0.8x = [-6 + 0.6x] + -4 Reorder the terms: 0.2 + 0.8x = -6 + -4 + 0.6x Combine like terms: -6 + -4 = -10 0.2 + 0.8x = -10 + 0.6x Solving 0.2 + 0.8x = -10 + 0.6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6x' to each side of the equation. 0.2 + 0.8x + -0.6x = -10 + 0.6x + -0.6x Combine like terms: 0.8x + -0.6x = 0.2x 0.2 + 0.2x = -10 + 0.6x + -0.6x Combine like terms: 0.6x + -0.6x = 0.0 0.2 + 0.2x = -10 + 0.0 0.2 + 0.2x = -10 Add '-0.2' to each side of the equation. 0.2 + -0.2 + 0.2x = -10 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.2x = -10 + -0.2 0.2x = -10 + -0.2 Combine like terms: -10 + -0.2 = -10.2 0.2x = -10.2 Divide each side by '0.2'. x = -51 Simplifying x = -51
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