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Simplifying 0.5x + 0.7(4 + x) = 0.25(7 + -4x) + 0.1x 0.5x + (4 * 0.7 + x * 0.7) = 0.25(7 + -4x) + 0.1x 0.5x + (2.8 + 0.7x) = 0.25(7 + -4x) + 0.1x Reorder the terms: 2.8 + 0.5x + 0.7x = 0.25(7 + -4x) + 0.1x Combine like terms: 0.5x + 0.7x = 1.2x 2.8 + 1.2x = 0.25(7 + -4x) + 0.1x 2.8 + 1.2x = (7 * 0.25 + -4x * 0.25) + 0.1x 2.8 + 1.2x = (1.75 + -1x) + 0.1x Combine like terms: -1x + 0.1x = -0.9x 2.8 + 1.2x = 1.75 + -0.9x Solving 2.8 + 1.2x = 1.75 + -0.9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9x' to each side of the equation. 2.8 + 1.2x + 0.9x = 1.75 + -0.9x + 0.9x Combine like terms: 1.2x + 0.9x = 2.1x 2.8 + 2.1x = 1.75 + -0.9x + 0.9x Combine like terms: -0.9x + 0.9x = 0.0 2.8 + 2.1x = 1.75 + 0.0 2.8 + 2.1x = 1.75 Add '-2.8' to each side of the equation. 2.8 + -2.8 + 2.1x = 1.75 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 2.1x = 1.75 + -2.8 2.1x = 1.75 + -2.8 Combine like terms: 1.75 + -2.8 = -1.05 2.1x = -1.05 Divide each side by '2.1'. x = -0.5 Simplifying x = -0.5
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