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Simplifying 0.5x + -0.1 = 0.4 + -0.9(4 + -4x) Reorder the terms: -0.1 + 0.5x = 0.4 + -0.9(4 + -4x) -0.1 + 0.5x = 0.4 + (4 * -0.9 + -4x * -0.9) -0.1 + 0.5x = 0.4 + (-3.6 + 3.6x) Combine like terms: 0.4 + -3.6 = -3.2 -0.1 + 0.5x = -3.2 + 3.6x Solving -0.1 + 0.5x = -3.2 + 3.6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6x' to each side of the equation. -0.1 + 0.5x + -3.6x = -3.2 + 3.6x + -3.6x Combine like terms: 0.5x + -3.6x = -3.1x -0.1 + -3.1x = -3.2 + 3.6x + -3.6x Combine like terms: 3.6x + -3.6x = 0.0 -0.1 + -3.1x = -3.2 + 0.0 -0.1 + -3.1x = -3.2 Add '0.1' to each side of the equation. -0.1 + 0.1 + -3.1x = -3.2 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -3.1x = -3.2 + 0.1 -3.1x = -3.2 + 0.1 Combine like terms: -3.2 + 0.1 = -3.1 -3.1x = -3.1 Divide each side by '-3.1'. x = 1 Simplifying x = 1
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