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Simplifying 4(2z + -4) + 18 + -3(z + 9) + 2z = 24 + (10z + -14) Reorder the terms: 4(-4 + 2z) + 18 + -3(z + 9) + 2z = 24 + (10z + -14) (-4 * 4 + 2z * 4) + 18 + -3(z + 9) + 2z = 24 + (10z + -14) (-16 + 8z) + 18 + -3(z + 9) + 2z = 24 + (10z + -14) Reorder the terms: -16 + 8z + 18 + -3(9 + z) + 2z = 24 + (10z + -14) -16 + 8z + 18 + (9 * -3 + z * -3) + 2z = 24 + (10z + -14) -16 + 8z + 18 + (-27 + -3z) + 2z = 24 + (10z + -14) Reorder the terms: -16 + 18 + -27 + 8z + -3z + 2z = 24 + (10z + -14) Combine like terms: -16 + 18 = 2 2 + -27 + 8z + -3z + 2z = 24 + (10z + -14) Combine like terms: 2 + -27 = -25 -25 + 8z + -3z + 2z = 24 + (10z + -14) Combine like terms: 8z + -3z = 5z -25 + 5z + 2z = 24 + (10z + -14) Combine like terms: 5z + 2z = 7z -25 + 7z = 24 + (10z + -14) Reorder the terms: -25 + 7z = 24 + (-14 + 10z) Remove parenthesis around (-14 + 10z) -25 + 7z = 24 + -14 + 10z Combine like terms: 24 + -14 = 10 -25 + 7z = 10 + 10z Solving -25 + 7z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. -25 + 7z + -10z = 10 + 10z + -10z Combine like terms: 7z + -10z = -3z -25 + -3z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -25 + -3z = 10 + 0 -25 + -3z = 10 Add '25' to each side of the equation. -25 + 25 + -3z = 10 + 25 Combine like terms: -25 + 25 = 0 0 + -3z = 10 + 25 -3z = 10 + 25 Combine like terms: 10 + 25 = 35 -3z = 35 Divide each side by '-3'. z = -11.66666667 Simplifying z = -11.66666667
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