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Simplifying 4(3z + -1) + -3(2 + 6) = 5(z + 1) Reorder the terms: 4(-1 + 3z) + -3(2 + 6) = 5(z + 1) (-1 * 4 + 3z * 4) + -3(2 + 6) = 5(z + 1) (-4 + 12z) + -3(2 + 6) = 5(z + 1) Combine like terms: 2 + 6 = 8 -4 + 12z + -3(8) = 5(z + 1) Multiply -3 * 8 -4 + 12z + -24 = 5(z + 1) Reorder the terms: -4 + -24 + 12z = 5(z + 1) Combine like terms: -4 + -24 = -28 -28 + 12z = 5(z + 1) Reorder the terms: -28 + 12z = 5(1 + z) -28 + 12z = (1 * 5 + z * 5) -28 + 12z = (5 + 5z) Solving -28 + 12z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -28 + 12z + -5z = 5 + 5z + -5z Combine like terms: 12z + -5z = 7z -28 + 7z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -28 + 7z = 5 + 0 -28 + 7z = 5 Add '28' to each side of the equation. -28 + 28 + 7z = 5 + 28 Combine like terms: -28 + 28 = 0 0 + 7z = 5 + 28 7z = 5 + 28 Combine like terms: 5 + 28 = 33 7z = 33 Divide each side by '7'. z = 4.714285714 Simplifying z = 4.714285714
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