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Simplifying 5(3z + -1) + -2(z + 4) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -2(z + 4) = 8(z + 1) (-1 * 5 + 3z * 5) + -2(z + 4) = 8(z + 1) (-5 + 15z) + -2(z + 4) = 8(z + 1) Reorder the terms: -5 + 15z + -2(4 + z) = 8(z + 1) -5 + 15z + (4 * -2 + z * -2) = 8(z + 1) -5 + 15z + (-8 + -2z) = 8(z + 1) Reorder the terms: -5 + -8 + 15z + -2z = 8(z + 1) Combine like terms: -5 + -8 = -13 -13 + 15z + -2z = 8(z + 1) Combine like terms: 15z + -2z = 13z -13 + 13z = 8(z + 1) Reorder the terms: -13 + 13z = 8(1 + z) -13 + 13z = (1 * 8 + z * 8) -13 + 13z = (8 + 8z) Solving -13 + 13z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -13 + 13z + -8z = 8 + 8z + -8z Combine like terms: 13z + -8z = 5z -13 + 5z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -13 + 5z = 8 + 0 -13 + 5z = 8 Add '13' to each side of the equation. -13 + 13 + 5z = 8 + 13 Combine like terms: -13 + 13 = 0 0 + 5z = 8 + 13 5z = 8 + 13 Combine like terms: 8 + 13 = 21 5z = 21 Divide each side by '5'. z = 4.2 Simplifying z = 4.2
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