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Simplifying 4(3z + -1) + -2(z + 1) = 7(z + 1) Reorder the terms: 4(-1 + 3z) + -2(z + 1) = 7(z + 1) (-1 * 4 + 3z * 4) + -2(z + 1) = 7(z + 1) (-4 + 12z) + -2(z + 1) = 7(z + 1) Reorder the terms: -4 + 12z + -2(1 + z) = 7(z + 1) -4 + 12z + (1 * -2 + z * -2) = 7(z + 1) -4 + 12z + (-2 + -2z) = 7(z + 1) Reorder the terms: -4 + -2 + 12z + -2z = 7(z + 1) Combine like terms: -4 + -2 = -6 -6 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -6 + 10z = 7(z + 1) Reorder the terms: -6 + 10z = 7(1 + z) -6 + 10z = (1 * 7 + z * 7) -6 + 10z = (7 + 7z) Solving -6 + 10z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -6 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -6 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -6 + 3z = 7 + 0 -6 + 3z = 7 Add '6' to each side of the equation. -6 + 6 + 3z = 7 + 6 Combine like terms: -6 + 6 = 0 0 + 3z = 7 + 6 3z = 7 + 6 Combine like terms: 7 + 6 = 13 3z = 13 Divide each side by '3'. z = 4.333333333 Simplifying z = 4.333333333
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