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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 Reorder the terms for easier multiplication: 0.2 + 0.8x = 3 * 4[-2 + 0.2x] Multiply 3 * 4 0.2 + 0.8x = 12[-2 + 0.2x] 0.2 + 0.8x = [-2 * 12 + 0.2x * 12] 0.2 + 0.8x = [-24 + 2.4x] Solving 0.2 + 0.8x = -24 + 2.4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4x' to each side of the equation. 0.2 + 0.8x + -2.4x = -24 + 2.4x + -2.4x Combine like terms: 0.8x + -2.4x = -1.6x 0.2 + -1.6x = -24 + 2.4x + -2.4x Combine like terms: 2.4x + -2.4x = 0.0 0.2 + -1.6x = -24 + 0.0 0.2 + -1.6x = -24 Add '-0.2' to each side of the equation. 0.2 + -0.2 + -1.6x = -24 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.6x = -24 + -0.2 -1.6x = -24 + -0.2 Combine like terms: -24 + -0.2 = -24.2 -1.6x = -24.2 Divide each side by '-1.6'. x = 15.125 Simplifying x = 15.125
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