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Simplifying 4(3z + 1) + -5(z + 8) = 3(z + 1) Reorder the terms: 4(1 + 3z) + -5(z + 8) = 3(z + 1) (1 * 4 + 3z * 4) + -5(z + 8) = 3(z + 1) (4 + 12z) + -5(z + 8) = 3(z + 1) Reorder the terms: 4 + 12z + -5(8 + z) = 3(z + 1) 4 + 12z + (8 * -5 + z * -5) = 3(z + 1) 4 + 12z + (-40 + -5z) = 3(z + 1) Reorder the terms: 4 + -40 + 12z + -5z = 3(z + 1) Combine like terms: 4 + -40 = -36 -36 + 12z + -5z = 3(z + 1) Combine like terms: 12z + -5z = 7z -36 + 7z = 3(z + 1) Reorder the terms: -36 + 7z = 3(1 + z) -36 + 7z = (1 * 3 + z * 3) -36 + 7z = (3 + 3z) Solving -36 + 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. -36 + 7z + -3z = 3 + 3z + -3z Combine like terms: 7z + -3z = 4z -36 + 4z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -36 + 4z = 3 + 0 -36 + 4z = 3 Add '36' to each side of the equation. -36 + 36 + 4z = 3 + 36 Combine like terms: -36 + 36 = 0 0 + 4z = 3 + 36 4z = 3 + 36 Combine like terms: 3 + 36 = 39 4z = 39 Divide each side by '4'. z = 9.75 Simplifying z = 9.75
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