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Simplifying 6(4z + 3) + -10(7z + -1) = 3(2 + -19z) Reorder the terms: 6(3 + 4z) + -10(7z + -1) = 3(2 + -19z) (3 * 6 + 4z * 6) + -10(7z + -1) = 3(2 + -19z) (18 + 24z) + -10(7z + -1) = 3(2 + -19z) Reorder the terms: 18 + 24z + -10(-1 + 7z) = 3(2 + -19z) 18 + 24z + (-1 * -10 + 7z * -10) = 3(2 + -19z) 18 + 24z + (10 + -70z) = 3(2 + -19z) Reorder the terms: 18 + 10 + 24z + -70z = 3(2 + -19z) Combine like terms: 18 + 10 = 28 28 + 24z + -70z = 3(2 + -19z) Combine like terms: 24z + -70z = -46z 28 + -46z = 3(2 + -19z) 28 + -46z = (2 * 3 + -19z * 3) 28 + -46z = (6 + -57z) Solving 28 + -46z = 6 + -57z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '57z' to each side of the equation. 28 + -46z + 57z = 6 + -57z + 57z Combine like terms: -46z + 57z = 11z 28 + 11z = 6 + -57z + 57z Combine like terms: -57z + 57z = 0 28 + 11z = 6 + 0 28 + 11z = 6 Add '-28' to each side of the equation. 28 + -28 + 11z = 6 + -28 Combine like terms: 28 + -28 = 0 0 + 11z = 6 + -28 11z = 6 + -28 Combine like terms: 6 + -28 = -22 11z = -22 Divide each side by '11'. z = -2 Simplifying z = -2
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