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Simplifying 10(z + 1) + -3(z + -1) = 3(z + -4) + 3(z + -2) Reorder the terms: 10(1 + z) + -3(z + -1) = 3(z + -4) + 3(z + -2) (1 * 10 + z * 10) + -3(z + -1) = 3(z + -4) + 3(z + -2) (10 + 10z) + -3(z + -1) = 3(z + -4) + 3(z + -2) Reorder the terms: 10 + 10z + -3(-1 + z) = 3(z + -4) + 3(z + -2) 10 + 10z + (-1 * -3 + z * -3) = 3(z + -4) + 3(z + -2) 10 + 10z + (3 + -3z) = 3(z + -4) + 3(z + -2) Reorder the terms: 10 + 3 + 10z + -3z = 3(z + -4) + 3(z + -2) Combine like terms: 10 + 3 = 13 13 + 10z + -3z = 3(z + -4) + 3(z + -2) Combine like terms: 10z + -3z = 7z 13 + 7z = 3(z + -4) + 3(z + -2) Reorder the terms: 13 + 7z = 3(-4 + z) + 3(z + -2) 13 + 7z = (-4 * 3 + z * 3) + 3(z + -2) 13 + 7z = (-12 + 3z) + 3(z + -2) Reorder the terms: 13 + 7z = -12 + 3z + 3(-2 + z) 13 + 7z = -12 + 3z + (-2 * 3 + z * 3) 13 + 7z = -12 + 3z + (-6 + 3z) Reorder the terms: 13 + 7z = -12 + -6 + 3z + 3z Combine like terms: -12 + -6 = -18 13 + 7z = -18 + 3z + 3z Combine like terms: 3z + 3z = 6z 13 + 7z = -18 + 6z Solving 13 + 7z = -18 + 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. 13 + 7z + -6z = -18 + 6z + -6z Combine like terms: 7z + -6z = 1z 13 + 1z = -18 + 6z + -6z Combine like terms: 6z + -6z = 0 13 + 1z = -18 + 0 13 + 1z = -18 Add '-13' to each side of the equation. 13 + -13 + 1z = -18 + -13 Combine like terms: 13 + -13 = 0 0 + 1z = -18 + -13 1z = -18 + -13 Combine like terms: -18 + -13 = -31 1z = -31 Divide each side by '1'. z = -31 Simplifying z = -31
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