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Simplifying 0.29(4x + 8y + -12z) = x + 2y + -3z (4x * 0.29 + 8y * 0.29 + -12z * 0.29) = x + 2y + -3z (1.16x + 2.32y + -3.48z) = x + 2y + -3z Solving 1.16x + 2.32y + -3.48z = x + 2y + -3z Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 1.16x + 2.32y + -1x + -3.48z = x + 2y + -1x + -3z Reorder the terms: 1.16x + -1x + 2.32y + -3.48z = x + 2y + -1x + -3z Combine like terms: 1.16x + -1x = 0.16x 0.16x + 2.32y + -3.48z = x + 2y + -1x + -3z Reorder the terms: 0.16x + 2.32y + -3.48z = x + -1x + 2y + -3z Combine like terms: x + -1x = 0 0.16x + 2.32y + -3.48z = 0 + 2y + -3z 0.16x + 2.32y + -3.48z = 2y + -3z Add '-2.32y' to each side of the equation. 0.16x + 2.32y + -2.32y + -3.48z = 2y + -2.32y + -3z Combine like terms: 2.32y + -2.32y = 0.00 0.16x + 0.00 + -3.48z = 2y + -2.32y + -3z 0.16x + -3.48z = 2y + -2.32y + -3z Combine like terms: 2y + -2.32y = -0.32y 0.16x + -3.48z = -0.32y + -3z Add '3.48z' to each side of the equation. 0.16x + -3.48z + 3.48z = -0.32y + -3z + 3.48z Combine like terms: -3.48z + 3.48z = 0.00 0.16x + 0.00 = -0.32y + -3z + 3.48z 0.16x = -0.32y + -3z + 3.48z Combine like terms: -3z + 3.48z = 0.48z 0.16x = -0.32y + 0.48z Divide each side by '0.16'. x = -2y + 3z Simplifying x = -2y + 3z
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