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Simplifying 5(z + 10) + 10 = 12(z + 3) + -10z Reorder the terms: 5(10 + z) + 10 = 12(z + 3) + -10z (10 * 5 + z * 5) + 10 = 12(z + 3) + -10z (50 + 5z) + 10 = 12(z + 3) + -10z Reorder the terms: 50 + 10 + 5z = 12(z + 3) + -10z Combine like terms: 50 + 10 = 60 60 + 5z = 12(z + 3) + -10z Reorder the terms: 60 + 5z = 12(3 + z) + -10z 60 + 5z = (3 * 12 + z * 12) + -10z 60 + 5z = (36 + 12z) + -10z Combine like terms: 12z + -10z = 2z 60 + 5z = 36 + 2z Solving 60 + 5z = 36 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 60 + 5z + -2z = 36 + 2z + -2z Combine like terms: 5z + -2z = 3z 60 + 3z = 36 + 2z + -2z Combine like terms: 2z + -2z = 0 60 + 3z = 36 + 0 60 + 3z = 36 Add '-60' to each side of the equation. 60 + -60 + 3z = 36 + -60 Combine like terms: 60 + -60 = 0 0 + 3z = 36 + -60 3z = 36 + -60 Combine like terms: 36 + -60 = -24 3z = -24 Divide each side by '3'. z = -8 Simplifying z = -8
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