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Simplifying 10(z + 4) + -1(4z + -2) = 3(z + -1) + 2(z + -3) Reorder the terms: 10(4 + z) + -1(4z + -2) = 3(z + -1) + 2(z + -3) (4 * 10 + z * 10) + -1(4z + -2) = 3(z + -1) + 2(z + -3) (40 + 10z) + -1(4z + -2) = 3(z + -1) + 2(z + -3) Reorder the terms: 40 + 10z + -1(-2 + 4z) = 3(z + -1) + 2(z + -3) 40 + 10z + (-2 * -1 + 4z * -1) = 3(z + -1) + 2(z + -3) 40 + 10z + (2 + -4z) = 3(z + -1) + 2(z + -3) Reorder the terms: 40 + 2 + 10z + -4z = 3(z + -1) + 2(z + -3) Combine like terms: 40 + 2 = 42 42 + 10z + -4z = 3(z + -1) + 2(z + -3) Combine like terms: 10z + -4z = 6z 42 + 6z = 3(z + -1) + 2(z + -3) Reorder the terms: 42 + 6z = 3(-1 + z) + 2(z + -3) 42 + 6z = (-1 * 3 + z * 3) + 2(z + -3) 42 + 6z = (-3 + 3z) + 2(z + -3) Reorder the terms: 42 + 6z = -3 + 3z + 2(-3 + z) 42 + 6z = -3 + 3z + (-3 * 2 + z * 2) 42 + 6z = -3 + 3z + (-6 + 2z) Reorder the terms: 42 + 6z = -3 + -6 + 3z + 2z Combine like terms: -3 + -6 = -9 42 + 6z = -9 + 3z + 2z Combine like terms: 3z + 2z = 5z 42 + 6z = -9 + 5z Solving 42 + 6z = -9 + 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. 42 + 6z + -5z = -9 + 5z + -5z Combine like terms: 6z + -5z = 1z 42 + 1z = -9 + 5z + -5z Combine like terms: 5z + -5z = 0 42 + 1z = -9 + 0 42 + 1z = -9 Add '-42' to each side of the equation. 42 + -42 + 1z = -9 + -42 Combine like terms: 42 + -42 = 0 0 + 1z = -9 + -42 1z = -9 + -42 Combine like terms: -9 + -42 = -51 1z = -51 Divide each side by '1'. z = -51 Simplifying z = -51
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