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Simplifying 0.5(x + -0.2) + 0.8x = 0.4(x + 1.2) + -2.47 Reorder the terms: 0.5(-0.2 + x) + 0.8x = 0.4(x + 1.2) + -2.47 (-0.2 * 0.5 + x * 0.5) + 0.8x = 0.4(x + 1.2) + -2.47 (-0.1 + 0.5x) + 0.8x = 0.4(x + 1.2) + -2.47 Combine like terms: 0.5x + 0.8x = 1.3x -0.1 + 1.3x = 0.4(x + 1.2) + -2.47 Reorder the terms: -0.1 + 1.3x = 0.4(1.2 + x) + -2.47 -0.1 + 1.3x = (1.2 * 0.4 + x * 0.4) + -2.47 -0.1 + 1.3x = (0.48 + 0.4x) + -2.47 Reorder the terms: -0.1 + 1.3x = 0.48 + -2.47 + 0.4x Combine like terms: 0.48 + -2.47 = -1.99 -0.1 + 1.3x = -1.99 + 0.4x Solving -0.1 + 1.3x = -1.99 + 0.4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4x' to each side of the equation. -0.1 + 1.3x + -0.4x = -1.99 + 0.4x + -0.4x Combine like terms: 1.3x + -0.4x = 0.9x -0.1 + 0.9x = -1.99 + 0.4x + -0.4x Combine like terms: 0.4x + -0.4x = 0.0 -0.1 + 0.9x = -1.99 + 0.0 -0.1 + 0.9x = -1.99 Add '0.1' to each side of the equation. -0.1 + 0.1 + 0.9x = -1.99 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.9x = -1.99 + 0.1 0.9x = -1.99 + 0.1 Combine like terms: -1.99 + 0.1 = -1.89 0.9x = -1.89 Divide each side by '0.9'. x = -2.1 Simplifying x = -2.1
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