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Simplifying 3(6z + -1) + -5(z + 8) = 10(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 8) = 10(z + 1) (-1 * 3 + 6z * 3) + -5(z + 8) = 10(z + 1) (-3 + 18z) + -5(z + 8) = 10(z + 1) Reorder the terms: -3 + 18z + -5(8 + z) = 10(z + 1) -3 + 18z + (8 * -5 + z * -5) = 10(z + 1) -3 + 18z + (-40 + -5z) = 10(z + 1) Reorder the terms: -3 + -40 + 18z + -5z = 10(z + 1) Combine like terms: -3 + -40 = -43 -43 + 18z + -5z = 10(z + 1) Combine like terms: 18z + -5z = 13z -43 + 13z = 10(z + 1) Reorder the terms: -43 + 13z = 10(1 + z) -43 + 13z = (1 * 10 + z * 10) -43 + 13z = (10 + 10z) Solving -43 + 13z = 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. -43 + 13z + -10z = 10 + 10z + -10z Combine like terms: 13z + -10z = 3z -43 + 3z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -43 + 3z = 10 + 0 -43 + 3z = 10 Add '43' to each side of the equation. -43 + 43 + 3z = 10 + 43 Combine like terms: -43 + 43 = 0 0 + 3z = 10 + 43 3z = 10 + 43 Combine like terms: 10 + 43 = 53 3z = 53 Divide each side by '3'. z = 17.66666667 Simplifying z = 17.66666667
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