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Simplifying 5(3z + -1) + -4(z + 2) = 6(z + 1) Reorder the terms: 5(-1 + 3z) + -4(z + 2) = 6(z + 1) (-1 * 5 + 3z * 5) + -4(z + 2) = 6(z + 1) (-5 + 15z) + -4(z + 2) = 6(z + 1) Reorder the terms: -5 + 15z + -4(2 + z) = 6(z + 1) -5 + 15z + (2 * -4 + z * -4) = 6(z + 1) -5 + 15z + (-8 + -4z) = 6(z + 1) Reorder the terms: -5 + -8 + 15z + -4z = 6(z + 1) Combine like terms: -5 + -8 = -13 -13 + 15z + -4z = 6(z + 1) Combine like terms: 15z + -4z = 11z -13 + 11z = 6(z + 1) Reorder the terms: -13 + 11z = 6(1 + z) -13 + 11z = (1 * 6 + z * 6) -13 + 11z = (6 + 6z) Solving -13 + 11z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -13 + 11z + -6z = 6 + 6z + -6z Combine like terms: 11z + -6z = 5z -13 + 5z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -13 + 5z = 6 + 0 -13 + 5z = 6 Add '13' to each side of the equation. -13 + 13 + 5z = 6 + 13 Combine like terms: -13 + 13 = 0 0 + 5z = 6 + 13 5z = 6 + 13 Combine like terms: 6 + 13 = 19 5z = 19 Divide each side by '5'. z = 3.8 Simplifying z = 3.8
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