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Simplifying 0.5(x + -12) + 0.2(x + 7) = 0.3x + 3.4 Reorder the terms: 0.5(-12 + x) + 0.2(x + 7) = 0.3x + 3.4 (-12 * 0.5 + x * 0.5) + 0.2(x + 7) = 0.3x + 3.4 (-6 + 0.5x) + 0.2(x + 7) = 0.3x + 3.4 Reorder the terms: -6 + 0.5x + 0.2(7 + x) = 0.3x + 3.4 -6 + 0.5x + (7 * 0.2 + x * 0.2) = 0.3x + 3.4 -6 + 0.5x + (1.4 + 0.2x) = 0.3x + 3.4 Reorder the terms: -6 + 1.4 + 0.5x + 0.2x = 0.3x + 3.4 Combine like terms: -6 + 1.4 = -4.6 -4.6 + 0.5x + 0.2x = 0.3x + 3.4 Combine like terms: 0.5x + 0.2x = 0.7x -4.6 + 0.7x = 0.3x + 3.4 Reorder the terms: -4.6 + 0.7x = 3.4 + 0.3x Solving -4.6 + 0.7x = 3.4 + 0.3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3x' to each side of the equation. -4.6 + 0.7x + -0.3x = 3.4 + 0.3x + -0.3x Combine like terms: 0.7x + -0.3x = 0.4x -4.6 + 0.4x = 3.4 + 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 -4.6 + 0.4x = 3.4 + 0.0 -4.6 + 0.4x = 3.4 Add '4.6' to each side of the equation. -4.6 + 4.6 + 0.4x = 3.4 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + 0.4x = 3.4 + 4.6 0.4x = 3.4 + 4.6 Combine like terms: 3.4 + 4.6 = 8 0.4x = 8 Divide each side by '0.4'. x = 20 Simplifying x = 20
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