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Simplifying 3(4z + -1) + -5(z + 3) = 3(z + 1) Reorder the terms: 3(-1 + 4z) + -5(z + 3) = 3(z + 1) (-1 * 3 + 4z * 3) + -5(z + 3) = 3(z + 1) (-3 + 12z) + -5(z + 3) = 3(z + 1) Reorder the terms: -3 + 12z + -5(3 + z) = 3(z + 1) -3 + 12z + (3 * -5 + z * -5) = 3(z + 1) -3 + 12z + (-15 + -5z) = 3(z + 1) Reorder the terms: -3 + -15 + 12z + -5z = 3(z + 1) Combine like terms: -3 + -15 = -18 -18 + 12z + -5z = 3(z + 1) Combine like terms: 12z + -5z = 7z -18 + 7z = 3(z + 1) Reorder the terms: -18 + 7z = 3(1 + z) -18 + 7z = (1 * 3 + z * 3) -18 + 7z = (3 + 3z) Solving -18 + 7z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -18 + 7z + -3z = 3 + 3z + -3z Combine like terms: 7z + -3z = 4z -18 + 4z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -18 + 4z = 3 + 0 -18 + 4z = 3 Add '18' to each side of the equation. -18 + 18 + 4z = 3 + 18 Combine like terms: -18 + 18 = 0 0 + 4z = 3 + 18 4z = 3 + 18 Combine like terms: 3 + 18 = 21 4z = 21 Divide each side by '4'. z = 5.25 Simplifying z = 5.25
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