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Simplifying 2(4z) + -3(5z + 2) = 4[10 + -1(z + 1)] Remove parenthesis around (4z) 2 * 4z + -3(5z + 2) = 4[10 + -1(z + 1)] Multiply 2 * 4 8z + -3(5z + 2) = 4[10 + -1(z + 1)] Reorder the terms: 8z + -3(2 + 5z) = 4[10 + -1(z + 1)] 8z + (2 * -3 + 5z * -3) = 4[10 + -1(z + 1)] 8z + (-6 + -15z) = 4[10 + -1(z + 1)] Reorder the terms: -6 + 8z + -15z = 4[10 + -1(z + 1)] Combine like terms: 8z + -15z = -7z -6 + -7z = 4[10 + -1(z + 1)] Reorder the terms: -6 + -7z = 4[10 + -1(1 + z)] -6 + -7z = 4[10 + (1 * -1 + z * -1)] -6 + -7z = 4[10 + (-1 + -1z)] Combine like terms: 10 + -1 = 9 -6 + -7z = 4[9 + -1z] -6 + -7z = [9 * 4 + -1z * 4] -6 + -7z = [36 + -4z] Solving -6 + -7z = 36 + -4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4z' to each side of the equation. -6 + -7z + 4z = 36 + -4z + 4z Combine like terms: -7z + 4z = -3z -6 + -3z = 36 + -4z + 4z Combine like terms: -4z + 4z = 0 -6 + -3z = 36 + 0 -6 + -3z = 36 Add '6' to each side of the equation. -6 + 6 + -3z = 36 + 6 Combine like terms: -6 + 6 = 0 0 + -3z = 36 + 6 -3z = 36 + 6 Combine like terms: 36 + 6 = 42 -3z = 42 Divide each side by '-3'. z = -14 Simplifying z = -14
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