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Simplifying 4(5z + -1) + -2(z + 3) = 7(z + 1) Reorder the terms: 4(-1 + 5z) + -2(z + 3) = 7(z + 1) (-1 * 4 + 5z * 4) + -2(z + 3) = 7(z + 1) (-4 + 20z) + -2(z + 3) = 7(z + 1) Reorder the terms: -4 + 20z + -2(3 + z) = 7(z + 1) -4 + 20z + (3 * -2 + z * -2) = 7(z + 1) -4 + 20z + (-6 + -2z) = 7(z + 1) Reorder the terms: -4 + -6 + 20z + -2z = 7(z + 1) Combine like terms: -4 + -6 = -10 -10 + 20z + -2z = 7(z + 1) Combine like terms: 20z + -2z = 18z -10 + 18z = 7(z + 1) Reorder the terms: -10 + 18z = 7(1 + z) -10 + 18z = (1 * 7 + z * 7) -10 + 18z = (7 + 7z) Solving -10 + 18z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -10 + 18z + -7z = 7 + 7z + -7z Combine like terms: 18z + -7z = 11z -10 + 11z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -10 + 11z = 7 + 0 -10 + 11z = 7 Add '10' to each side of the equation. -10 + 10 + 11z = 7 + 10 Combine like terms: -10 + 10 = 0 0 + 11z = 7 + 10 11z = 7 + 10 Combine like terms: 7 + 10 = 17 11z = 17 Divide each side by '11'. z = 1.545454545 Simplifying z = 1.545454545
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