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Simplifying 10(z + 1) + -3(z + -3) = 4(z + -2) + 2(z + -4) Reorder the terms: 10(1 + z) + -3(z + -3) = 4(z + -2) + 2(z + -4) (1 * 10 + z * 10) + -3(z + -3) = 4(z + -2) + 2(z + -4) (10 + 10z) + -3(z + -3) = 4(z + -2) + 2(z + -4) Reorder the terms: 10 + 10z + -3(-3 + z) = 4(z + -2) + 2(z + -4) 10 + 10z + (-3 * -3 + z * -3) = 4(z + -2) + 2(z + -4) 10 + 10z + (9 + -3z) = 4(z + -2) + 2(z + -4) Reorder the terms: 10 + 9 + 10z + -3z = 4(z + -2) + 2(z + -4) Combine like terms: 10 + 9 = 19 19 + 10z + -3z = 4(z + -2) + 2(z + -4) Combine like terms: 10z + -3z = 7z 19 + 7z = 4(z + -2) + 2(z + -4) Reorder the terms: 19 + 7z = 4(-2 + z) + 2(z + -4) 19 + 7z = (-2 * 4 + z * 4) + 2(z + -4) 19 + 7z = (-8 + 4z) + 2(z + -4) Reorder the terms: 19 + 7z = -8 + 4z + 2(-4 + z) 19 + 7z = -8 + 4z + (-4 * 2 + z * 2) 19 + 7z = -8 + 4z + (-8 + 2z) Reorder the terms: 19 + 7z = -8 + -8 + 4z + 2z Combine like terms: -8 + -8 = -16 19 + 7z = -16 + 4z + 2z Combine like terms: 4z + 2z = 6z 19 + 7z = -16 + 6z Solving 19 + 7z = -16 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 19 + 7z + -6z = -16 + 6z + -6z Combine like terms: 7z + -6z = 1z 19 + 1z = -16 + 6z + -6z Combine like terms: 6z + -6z = 0 19 + 1z = -16 + 0 19 + 1z = -16 Add '-19' to each side of the equation. 19 + -19 + 1z = -16 + -19 Combine like terms: 19 + -19 = 0 0 + 1z = -16 + -19 1z = -16 + -19 Combine like terms: -16 + -19 = -35 1z = -35 Divide each side by '1'. z = -35 Simplifying z = -35
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