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Simplifying -2 + -5(2z + 9) = 4(8z + -7) + 1 Reorder the terms: -2 + -5(9 + 2z) = 4(8z + -7) + 1 -2 + (9 * -5 + 2z * -5) = 4(8z + -7) + 1 -2 + (-45 + -10z) = 4(8z + -7) + 1 Combine like terms: -2 + -45 = -47 -47 + -10z = 4(8z + -7) + 1 Reorder the terms: -47 + -10z = 4(-7 + 8z) + 1 -47 + -10z = (-7 * 4 + 8z * 4) + 1 -47 + -10z = (-28 + 32z) + 1 Reorder the terms: -47 + -10z = -28 + 1 + 32z Combine like terms: -28 + 1 = -27 -47 + -10z = -27 + 32z Solving -47 + -10z = -27 + 32z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-32z' to each side of the equation. -47 + -10z + -32z = -27 + 32z + -32z Combine like terms: -10z + -32z = -42z -47 + -42z = -27 + 32z + -32z Combine like terms: 32z + -32z = 0 -47 + -42z = -27 + 0 -47 + -42z = -27 Add '47' to each side of the equation. -47 + 47 + -42z = -27 + 47 Combine like terms: -47 + 47 = 0 0 + -42z = -27 + 47 -42z = -27 + 47 Combine like terms: -27 + 47 = 20 -42z = 20 Divide each side by '-42'. z = -0.4761904762 Simplifying z = -0.4761904762
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