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Simplifying 0.4x + 0.7(0.3x + 4) = 0.6(0.4x + -0.1) + -0.1 Reorder the terms: 0.4x + 0.7(4 + 0.3x) = 0.6(0.4x + -0.1) + -0.1 0.4x + (4 * 0.7 + 0.3x * 0.7) = 0.6(0.4x + -0.1) + -0.1 0.4x + (2.8 + 0.21x) = 0.6(0.4x + -0.1) + -0.1 Reorder the terms: 2.8 + 0.4x + 0.21x = 0.6(0.4x + -0.1) + -0.1 Combine like terms: 0.4x + 0.21x = 0.61x 2.8 + 0.61x = 0.6(0.4x + -0.1) + -0.1 Reorder the terms: 2.8 + 0.61x = 0.6(-0.1 + 0.4x) + -0.1 2.8 + 0.61x = (-0.1 * 0.6 + 0.4x * 0.6) + -0.1 2.8 + 0.61x = (-0.06 + 0.24x) + -0.1 Reorder the terms: 2.8 + 0.61x = -0.06 + -0.1 + 0.24x Combine like terms: -0.06 + -0.1 = -0.16 2.8 + 0.61x = -0.16 + 0.24x Solving 2.8 + 0.61x = -0.16 + 0.24x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.24x' to each side of the equation. 2.8 + 0.61x + -0.24x = -0.16 + 0.24x + -0.24x Combine like terms: 0.61x + -0.24x = 0.37x 2.8 + 0.37x = -0.16 + 0.24x + -0.24x Combine like terms: 0.24x + -0.24x = 0.00 2.8 + 0.37x = -0.16 + 0.00 2.8 + 0.37x = -0.16 Add '-2.8' to each side of the equation. 2.8 + -2.8 + 0.37x = -0.16 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 0.37x = -0.16 + -2.8 0.37x = -0.16 + -2.8 Combine like terms: -0.16 + -2.8 = -2.96 0.37x = -2.96 Divide each side by '0.37'. x = -8 Simplifying x = -8
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