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Simplifying 3(6z + -1) + -2(z + 2) = 10(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 2) = 10(z + 1) (-1 * 3 + 6z * 3) + -2(z + 2) = 10(z + 1) (-3 + 18z) + -2(z + 2) = 10(z + 1) Reorder the terms: -3 + 18z + -2(2 + z) = 10(z + 1) -3 + 18z + (2 * -2 + z * -2) = 10(z + 1) -3 + 18z + (-4 + -2z) = 10(z + 1) Reorder the terms: -3 + -4 + 18z + -2z = 10(z + 1) Combine like terms: -3 + -4 = -7 -7 + 18z + -2z = 10(z + 1) Combine like terms: 18z + -2z = 16z -7 + 16z = 10(z + 1) Reorder the terms: -7 + 16z = 10(1 + z) -7 + 16z = (1 * 10 + z * 10) -7 + 16z = (10 + 10z) Solving -7 + 16z = 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. -7 + 16z + -10z = 10 + 10z + -10z Combine like terms: 16z + -10z = 6z -7 + 6z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -7 + 6z = 10 + 0 -7 + 6z = 10 Add '7' to each side of the equation. -7 + 7 + 6z = 10 + 7 Combine like terms: -7 + 7 = 0 0 + 6z = 10 + 7 6z = 10 + 7 Combine like terms: 10 + 7 = 17 6z = 17 Divide each side by '6'. z = 2.833333333 Simplifying z = 2.833333333
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