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Simplifying 10 = 0.5(6x + -4) + 0.75(8x + 4) Reorder the terms: 10 = 0.5(-4 + 6x) + 0.75(8x + 4) 10 = (-4 * 0.5 + 6x * 0.5) + 0.75(8x + 4) 10 = (-2 + 3x) + 0.75(8x + 4) Reorder the terms: 10 = -2 + 3x + 0.75(4 + 8x) 10 = -2 + 3x + (4 * 0.75 + 8x * 0.75) 10 = -2 + 3x + (3 + 6x) Reorder the terms: 10 = -2 + 3 + 3x + 6x Combine like terms: -2 + 3 = 1 10 = 1 + 3x + 6x Combine like terms: 3x + 6x = 9x 10 = 1 + 9x Solving 10 = 1 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. 10 + -9x = 1 + 9x + -9x Combine like terms: 9x + -9x = 0 10 + -9x = 1 + 0 10 + -9x = 1 Add '-10' to each side of the equation. 10 + -10 + -9x = 1 + -10 Combine like terms: 10 + -10 = 0 0 + -9x = 1 + -10 -9x = 1 + -10 Combine like terms: 1 + -10 = -9 -9x = -9 Divide each side by '-9'. x = 1 Simplifying x = 1
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