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Simplifying 5(-1z + 7) + -4(3z + -2) = -1z + 5 + -4z Reorder the terms: 5(7 + -1z) + -4(3z + -2) = -1z + 5 + -4z (7 * 5 + -1z * 5) + -4(3z + -2) = -1z + 5 + -4z (35 + -5z) + -4(3z + -2) = -1z + 5 + -4z Reorder the terms: 35 + -5z + -4(-2 + 3z) = -1z + 5 + -4z 35 + -5z + (-2 * -4 + 3z * -4) = -1z + 5 + -4z 35 + -5z + (8 + -12z) = -1z + 5 + -4z Reorder the terms: 35 + 8 + -5z + -12z = -1z + 5 + -4z Combine like terms: 35 + 8 = 43 43 + -5z + -12z = -1z + 5 + -4z Combine like terms: -5z + -12z = -17z 43 + -17z = -1z + 5 + -4z Reorder the terms: 43 + -17z = 5 + -1z + -4z Combine like terms: -1z + -4z = -5z 43 + -17z = 5 + -5z Solving 43 + -17z = 5 + -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. 43 + -17z + 5z = 5 + -5z + 5z Combine like terms: -17z + 5z = -12z 43 + -12z = 5 + -5z + 5z Combine like terms: -5z + 5z = 0 43 + -12z = 5 + 0 43 + -12z = 5 Add '-43' to each side of the equation. 43 + -43 + -12z = 5 + -43 Combine like terms: 43 + -43 = 0 0 + -12z = 5 + -43 -12z = 5 + -43 Combine like terms: 5 + -43 = -38 -12z = -38 Divide each side by '-12'. z = 3.166666667 Simplifying z = 3.166666667
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