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Simplifying 5(4z + -1) + -2(z + 4) = 7(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 4) = 7(z + 1) (-1 * 5 + 4z * 5) + -2(z + 4) = 7(z + 1) (-5 + 20z) + -2(z + 4) = 7(z + 1) Reorder the terms: -5 + 20z + -2(4 + z) = 7(z + 1) -5 + 20z + (4 * -2 + z * -2) = 7(z + 1) -5 + 20z + (-8 + -2z) = 7(z + 1) Reorder the terms: -5 + -8 + 20z + -2z = 7(z + 1) Combine like terms: -5 + -8 = -13 -13 + 20z + -2z = 7(z + 1) Combine like terms: 20z + -2z = 18z -13 + 18z = 7(z + 1) Reorder the terms: -13 + 18z = 7(1 + z) -13 + 18z = (1 * 7 + z * 7) -13 + 18z = (7 + 7z) Solving -13 + 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. -13 + 18z + -7z = 7 + 7z + -7z Combine like terms: 18z + -7z = 11z -13 + 11z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -13 + 11z = 7 + 0 -13 + 11z = 7 Add '13' to each side of the equation. -13 + 13 + 11z = 7 + 13 Combine like terms: -13 + 13 = 0 0 + 11z = 7 + 13 11z = 7 + 13 Combine like terms: 7 + 13 = 20 11z = 20 Divide each side by '11'. z = 1.818181818 Simplifying z = 1.818181818
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