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Simplifying 0.4(x + -6) = 0.7(2x + 3) + 0.5 Reorder the terms: 0.4(-6 + x) = 0.7(2x + 3) + 0.5 (-6 * 0.4 + x * 0.4) = 0.7(2x + 3) + 0.5 (-2.4 + 0.4x) = 0.7(2x + 3) + 0.5 Reorder the terms: -2.4 + 0.4x = 0.7(3 + 2x) + 0.5 -2.4 + 0.4x = (3 * 0.7 + 2x * 0.7) + 0.5 -2.4 + 0.4x = (2.1 + 1.4x) + 0.5 Reorder the terms: -2.4 + 0.4x = 2.1 + 0.5 + 1.4x Combine like terms: 2.1 + 0.5 = 2.6 -2.4 + 0.4x = 2.6 + 1.4x Solving -2.4 + 0.4x = 2.6 + 1.4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4x' to each side of the equation. -2.4 + 0.4x + -1.4x = 2.6 + 1.4x + -1.4x Combine like terms: 0.4x + -1.4x = -1x -2.4 + -1x = 2.6 + 1.4x + -1.4x Combine like terms: 1.4x + -1.4x = 0.0 -2.4 + -1x = 2.6 + 0.0 -2.4 + -1x = 2.6 Add '2.4' to each side of the equation. -2.4 + 2.4 + -1x = 2.6 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1x = 2.6 + 2.4 -1x = 2.6 + 2.4 Combine like terms: 2.6 + 2.4 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5
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