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Simplifying 3(4z + -1) + -2(z + 2) = 2(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 2) = 2(z + 1) (-1 * 3 + 4z * 3) + -2(z + 2) = 2(z + 1) (-3 + 12z) + -2(z + 2) = 2(z + 1) Reorder the terms: -3 + 12z + -2(2 + z) = 2(z + 1) -3 + 12z + (2 * -2 + z * -2) = 2(z + 1) -3 + 12z + (-4 + -2z) = 2(z + 1) Reorder the terms: -3 + -4 + 12z + -2z = 2(z + 1) Combine like terms: -3 + -4 = -7 -7 + 12z + -2z = 2(z + 1) Combine like terms: 12z + -2z = 10z -7 + 10z = 2(z + 1) Reorder the terms: -7 + 10z = 2(1 + z) -7 + 10z = (1 * 2 + z * 2) -7 + 10z = (2 + 2z) Solving -7 + 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. -7 + 10z + -2z = 2 + 2z + -2z Combine like terms: 10z + -2z = 8z -7 + 8z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -7 + 8z = 2 + 0 -7 + 8z = 2 Add '7' to each side of the equation. -7 + 7 + 8z = 2 + 7 Combine like terms: -7 + 7 = 0 0 + 8z = 2 + 7 8z = 2 + 7 Combine like terms: 2 + 7 = 9 8z = 9 Divide each side by '8'. z = 1.125 Simplifying z = 1.125
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