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Simplifying 2(4z + -3) + -3(5z + 2) = 4(10 + -1z + 1) Reorder the terms: 2(-3 + 4z) + -3(5z + 2) = 4(10 + -1z + 1) (-3 * 2 + 4z * 2) + -3(5z + 2) = 4(10 + -1z + 1) (-6 + 8z) + -3(5z + 2) = 4(10 + -1z + 1) Reorder the terms: -6 + 8z + -3(2 + 5z) = 4(10 + -1z + 1) -6 + 8z + (2 * -3 + 5z * -3) = 4(10 + -1z + 1) -6 + 8z + (-6 + -15z) = 4(10 + -1z + 1) Reorder the terms: -6 + -6 + 8z + -15z = 4(10 + -1z + 1) Combine like terms: -6 + -6 = -12 -12 + 8z + -15z = 4(10 + -1z + 1) Combine like terms: 8z + -15z = -7z -12 + -7z = 4(10 + -1z + 1) Reorder the terms: -12 + -7z = 4(10 + 1 + -1z) Combine like terms: 10 + 1 = 11 -12 + -7z = 4(11 + -1z) -12 + -7z = (11 * 4 + -1z * 4) -12 + -7z = (44 + -4z) Solving -12 + -7z = 44 + -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. -12 + -7z + 4z = 44 + -4z + 4z Combine like terms: -7z + 4z = -3z -12 + -3z = 44 + -4z + 4z Combine like terms: -4z + 4z = 0 -12 + -3z = 44 + 0 -12 + -3z = 44 Add '12' to each side of the equation. -12 + 12 + -3z = 44 + 12 Combine like terms: -12 + 12 = 0 0 + -3z = 44 + 12 -3z = 44 + 12 Combine like terms: 44 + 12 = 56 -3z = 56 Divide each side by '-3'. z = -18.66666667 Simplifying z = -18.66666667
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