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Simplifying 3(4z + -1) + -5(z + 3) = (z + 1) Reorder the terms: 3(-1 + 4z) + -5(z + 3) = (z + 1) (-1 * 3 + 4z * 3) + -5(z + 3) = (z + 1) (-3 + 12z) + -5(z + 3) = (z + 1) Reorder the terms: -3 + 12z + -5(3 + z) = (z + 1) -3 + 12z + (3 * -5 + z * -5) = (z + 1) -3 + 12z + (-15 + -5z) = (z + 1) Reorder the terms: -3 + -15 + 12z + -5z = (z + 1) Combine like terms: -3 + -15 = -18 -18 + 12z + -5z = (z + 1) Combine like terms: 12z + -5z = 7z -18 + 7z = (z + 1) Reorder the terms: -18 + 7z = (1 + z) Remove parenthesis around (1 + z) -18 + 7z = 1 + z Solving -18 + 7z = 1 + z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. -18 + 7z + -1z = 1 + z + -1z Combine like terms: 7z + -1z = 6z -18 + 6z = 1 + z + -1z Combine like terms: z + -1z = 0 -18 + 6z = 1 + 0 -18 + 6z = 1 Add '18' to each side of the equation. -18 + 18 + 6z = 1 + 18 Combine like terms: -18 + 18 = 0 0 + 6z = 1 + 18 6z = 1 + 18 Combine like terms: 1 + 18 = 19 6z = 19 Divide each side by '6'. z = 3.166666667 Simplifying z = 3.166666667
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