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Simplifying 0.167(z + 3) = -0.5(z + 2) Reorder the terms: 0.167(3 + z) = -0.5(z + 2) (3 * 0.167 + z * 0.167) = -0.5(z + 2) (0.501 + 0.167z) = -0.5(z + 2) Reorder the terms: 0.501 + 0.167z = -0.5(2 + z) 0.501 + 0.167z = (2 * -0.5 + z * -0.5) 0.501 + 0.167z = (-1 + -0.5z) Solving 0.501 + 0.167z = -1 + -0.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5z' to each side of the equation. 0.501 + 0.167z + 0.5z = -1 + -0.5z + 0.5z Combine like terms: 0.167z + 0.5z = 0.667z 0.501 + 0.667z = -1 + -0.5z + 0.5z Combine like terms: -0.5z + 0.5z = 0.0 0.501 + 0.667z = -1 + 0.0 0.501 + 0.667z = -1 Add '-0.501' to each side of the equation. 0.501 + -0.501 + 0.667z = -1 + -0.501 Combine like terms: 0.501 + -0.501 = 0.000 0.000 + 0.667z = -1 + -0.501 0.667z = -1 + -0.501 Combine like terms: -1 + -0.501 = -1.501 0.667z = -1.501 Divide each side by '0.667'. z = -2.250374813 Simplifying z = -2.250374813
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