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Simplifying 5(4z + -2) + -3(z + 8) = 10(z + 1) Reorder the terms: 5(-2 + 4z) + -3(z + 8) = 10(z + 1) (-2 * 5 + 4z * 5) + -3(z + 8) = 10(z + 1) (-10 + 20z) + -3(z + 8) = 10(z + 1) Reorder the terms: -10 + 20z + -3(8 + z) = 10(z + 1) -10 + 20z + (8 * -3 + z * -3) = 10(z + 1) -10 + 20z + (-24 + -3z) = 10(z + 1) Reorder the terms: -10 + -24 + 20z + -3z = 10(z + 1) Combine like terms: -10 + -24 = -34 -34 + 20z + -3z = 10(z + 1) Combine like terms: 20z + -3z = 17z -34 + 17z = 10(z + 1) Reorder the terms: -34 + 17z = 10(1 + z) -34 + 17z = (1 * 10 + z * 10) -34 + 17z = (10 + 10z) Solving -34 + 17z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. -34 + 17z + -10z = 10 + 10z + -10z Combine like terms: 17z + -10z = 7z -34 + 7z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -34 + 7z = 10 + 0 -34 + 7z = 10 Add '34' to each side of the equation. -34 + 34 + 7z = 10 + 34 Combine like terms: -34 + 34 = 0 0 + 7z = 10 + 34 7z = 10 + 34 Combine like terms: 10 + 34 = 44 7z = 44 Divide each side by '7'. z = 6.285714286 Simplifying z = 6.285714286
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