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Simplifying 3(5z + -1) + -5(z + 2) = 2(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 2) = 2(z + 1) (-1 * 3 + 5z * 3) + -5(z + 2) = 2(z + 1) (-3 + 15z) + -5(z + 2) = 2(z + 1) Reorder the terms: -3 + 15z + -5(2 + z) = 2(z + 1) -3 + 15z + (2 * -5 + z * -5) = 2(z + 1) -3 + 15z + (-10 + -5z) = 2(z + 1) Reorder the terms: -3 + -10 + 15z + -5z = 2(z + 1) Combine like terms: -3 + -10 = -13 -13 + 15z + -5z = 2(z + 1) Combine like terms: 15z + -5z = 10z -13 + 10z = 2(z + 1) Reorder the terms: -13 + 10z = 2(1 + z) -13 + 10z = (1 * 2 + z * 2) -13 + 10z = (2 + 2z) Solving -13 + 10z = 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. -13 + 10z + -2z = 2 + 2z + -2z Combine like terms: 10z + -2z = 8z -13 + 8z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -13 + 8z = 2 + 0 -13 + 8z = 2 Add '13' to each side of the equation. -13 + 13 + 8z = 2 + 13 Combine like terms: -13 + 13 = 0 0 + 8z = 2 + 13 8z = 2 + 13 Combine like terms: 2 + 13 = 15 8z = 15 Divide each side by '8'. z = 1.875 Simplifying z = 1.875
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