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Simplifying 3(2z + -1) + 4(z + 3) = 5(2z + -1) + 4(3z + -1) Reorder the terms: 3(-1 + 2z) + 4(z + 3) = 5(2z + -1) + 4(3z + -1) (-1 * 3 + 2z * 3) + 4(z + 3) = 5(2z + -1) + 4(3z + -1) (-3 + 6z) + 4(z + 3) = 5(2z + -1) + 4(3z + -1) Reorder the terms: -3 + 6z + 4(3 + z) = 5(2z + -1) + 4(3z + -1) -3 + 6z + (3 * 4 + z * 4) = 5(2z + -1) + 4(3z + -1) -3 + 6z + (12 + 4z) = 5(2z + -1) + 4(3z + -1) Reorder the terms: -3 + 12 + 6z + 4z = 5(2z + -1) + 4(3z + -1) Combine like terms: -3 + 12 = 9 9 + 6z + 4z = 5(2z + -1) + 4(3z + -1) Combine like terms: 6z + 4z = 10z 9 + 10z = 5(2z + -1) + 4(3z + -1) Reorder the terms: 9 + 10z = 5(-1 + 2z) + 4(3z + -1) 9 + 10z = (-1 * 5 + 2z * 5) + 4(3z + -1) 9 + 10z = (-5 + 10z) + 4(3z + -1) Reorder the terms: 9 + 10z = -5 + 10z + 4(-1 + 3z) 9 + 10z = -5 + 10z + (-1 * 4 + 3z * 4) 9 + 10z = -5 + 10z + (-4 + 12z) Reorder the terms: 9 + 10z = -5 + -4 + 10z + 12z Combine like terms: -5 + -4 = -9 9 + 10z = -9 + 10z + 12z Combine like terms: 10z + 12z = 22z 9 + 10z = -9 + 22z Solving 9 + 10z = -9 + 22z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-22z' to each side of the equation. 9 + 10z + -22z = -9 + 22z + -22z Combine like terms: 10z + -22z = -12z 9 + -12z = -9 + 22z + -22z Combine like terms: 22z + -22z = 0 9 + -12z = -9 + 0 9 + -12z = -9 Add '-9' to each side of the equation. 9 + -9 + -12z = -9 + -9 Combine like terms: 9 + -9 = 0 0 + -12z = -9 + -9 -12z = -9 + -9 Combine like terms: -9 + -9 = -18 -12z = -18 Divide each side by '-12'. z = 1.5 Simplifying z = 1.5
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