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Simplifying 4(z + -2) = 7(3z + 6) + 1 Reorder the terms: 4(-2 + z) = 7(3z + 6) + 1 (-2 * 4 + z * 4) = 7(3z + 6) + 1 (-8 + 4z) = 7(3z + 6) + 1 Reorder the terms: -8 + 4z = 7(6 + 3z) + 1 -8 + 4z = (6 * 7 + 3z * 7) + 1 -8 + 4z = (42 + 21z) + 1 Reorder the terms: -8 + 4z = 42 + 1 + 21z Combine like terms: 42 + 1 = 43 -8 + 4z = 43 + 21z Solving -8 + 4z = 43 + 21z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-21z' to each side of the equation. -8 + 4z + -21z = 43 + 21z + -21z Combine like terms: 4z + -21z = -17z -8 + -17z = 43 + 21z + -21z Combine like terms: 21z + -21z = 0 -8 + -17z = 43 + 0 -8 + -17z = 43 Add '8' to each side of the equation. -8 + 8 + -17z = 43 + 8 Combine like terms: -8 + 8 = 0 0 + -17z = 43 + 8 -17z = 43 + 8 Combine like terms: 43 + 8 = 51 -17z = 51 Divide each side by '-17'. z = -3 Simplifying z = -3
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