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Simplifying 3(5z + -1) + -3(z + 4) = 2(z + 1) Reorder the terms: 3(-1 + 5z) + -3(z + 4) = 2(z + 1) (-1 * 3 + 5z * 3) + -3(z + 4) = 2(z + 1) (-3 + 15z) + -3(z + 4) = 2(z + 1) Reorder the terms: -3 + 15z + -3(4 + z) = 2(z + 1) -3 + 15z + (4 * -3 + z * -3) = 2(z + 1) -3 + 15z + (-12 + -3z) = 2(z + 1) Reorder the terms: -3 + -12 + 15z + -3z = 2(z + 1) Combine like terms: -3 + -12 = -15 -15 + 15z + -3z = 2(z + 1) Combine like terms: 15z + -3z = 12z -15 + 12z = 2(z + 1) Reorder the terms: -15 + 12z = 2(1 + z) -15 + 12z = (1 * 2 + z * 2) -15 + 12z = (2 + 2z) Solving -15 + 12z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -15 + 12z + -2z = 2 + 2z + -2z Combine like terms: 12z + -2z = 10z -15 + 10z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -15 + 10z = 2 + 0 -15 + 10z = 2 Add '15' to each side of the equation. -15 + 15 + 10z = 2 + 15 Combine like terms: -15 + 15 = 0 0 + 10z = 2 + 15 10z = 2 + 15 Combine like terms: 2 + 15 = 17 10z = 17 Divide each side by '10'. z = 1.7 Simplifying z = 1.7
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