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Simplifying 6(4z + -1) + -2(z + 3) = 19(z + 1) Reorder the terms: 6(-1 + 4z) + -2(z + 3) = 19(z + 1) (-1 * 6 + 4z * 6) + -2(z + 3) = 19(z + 1) (-6 + 24z) + -2(z + 3) = 19(z + 1) Reorder the terms: -6 + 24z + -2(3 + z) = 19(z + 1) -6 + 24z + (3 * -2 + z * -2) = 19(z + 1) -6 + 24z + (-6 + -2z) = 19(z + 1) Reorder the terms: -6 + -6 + 24z + -2z = 19(z + 1) Combine like terms: -6 + -6 = -12 -12 + 24z + -2z = 19(z + 1) Combine like terms: 24z + -2z = 22z -12 + 22z = 19(z + 1) Reorder the terms: -12 + 22z = 19(1 + z) -12 + 22z = (1 * 19 + z * 19) -12 + 22z = (19 + 19z) Solving -12 + 22z = 19 + 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. -12 + 22z + -19z = 19 + 19z + -19z Combine like terms: 22z + -19z = 3z -12 + 3z = 19 + 19z + -19z Combine like terms: 19z + -19z = 0 -12 + 3z = 19 + 0 -12 + 3z = 19 Add '12' to each side of the equation. -12 + 12 + 3z = 19 + 12 Combine like terms: -12 + 12 = 0 0 + 3z = 19 + 12 3z = 19 + 12 Combine like terms: 19 + 12 = 31 3z = 31 Divide each side by '3'. z = 10.33333333 Simplifying z = 10.33333333
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