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Simplifying 12z + 10z + (23z + -30) = 24 + -1(-19z + -20) Reorder the terms: 12z + 10z + (-30 + 23z) = 24 + -1(-19z + -20) Remove parenthesis around (-30 + 23z) 12z + 10z + -30 + 23z = 24 + -1(-19z + -20) Reorder the terms: -30 + 12z + 10z + 23z = 24 + -1(-19z + -20) Combine like terms: 12z + 10z = 22z -30 + 22z + 23z = 24 + -1(-19z + -20) Combine like terms: 22z + 23z = 45z -30 + 45z = 24 + -1(-19z + -20) Reorder the terms: -30 + 45z = 24 + -1(-20 + -19z) -30 + 45z = 24 + (-20 * -1 + -19z * -1) -30 + 45z = 24 + (20 + 19z) Combine like terms: 24 + 20 = 44 -30 + 45z = 44 + 19z Solving -30 + 45z = 44 + 19z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-19z' to each side of the equation. -30 + 45z + -19z = 44 + 19z + -19z Combine like terms: 45z + -19z = 26z -30 + 26z = 44 + 19z + -19z Combine like terms: 19z + -19z = 0 -30 + 26z = 44 + 0 -30 + 26z = 44 Add '30' to each side of the equation. -30 + 30 + 26z = 44 + 30 Combine like terms: -30 + 30 = 0 0 + 26z = 44 + 30 26z = 44 + 30 Combine like terms: 44 + 30 = 74 26z = 74 Divide each side by '26'. z = 2.846153846 Simplifying z = 2.846153846
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