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Simplifying 4(5z + -1) + -3(z + 2) = 6(z + 1) Reorder the terms: 4(-1 + 5z) + -3(z + 2) = 6(z + 1) (-1 * 4 + 5z * 4) + -3(z + 2) = 6(z + 1) (-4 + 20z) + -3(z + 2) = 6(z + 1) Reorder the terms: -4 + 20z + -3(2 + z) = 6(z + 1) -4 + 20z + (2 * -3 + z * -3) = 6(z + 1) -4 + 20z + (-6 + -3z) = 6(z + 1) Reorder the terms: -4 + -6 + 20z + -3z = 6(z + 1) Combine like terms: -4 + -6 = -10 -10 + 20z + -3z = 6(z + 1) Combine like terms: 20z + -3z = 17z -10 + 17z = 6(z + 1) Reorder the terms: -10 + 17z = 6(1 + z) -10 + 17z = (1 * 6 + z * 6) -10 + 17z = (6 + 6z) Solving -10 + 17z = 6 + 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. -10 + 17z + -6z = 6 + 6z + -6z Combine like terms: 17z + -6z = 11z -10 + 11z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -10 + 11z = 6 + 0 -10 + 11z = 6 Add '10' to each side of the equation. -10 + 10 + 11z = 6 + 10 Combine like terms: -10 + 10 = 0 0 + 11z = 6 + 10 11z = 6 + 10 Combine like terms: 6 + 10 = 16 11z = 16 Divide each side by '11'. z = 1.454545455 Simplifying z = 1.454545455
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