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Simplifying 13z + -8(z + 1) = 2(z + -3) + 3 Reorder the terms: 13z + -8(1 + z) = 2(z + -3) + 3 13z + (1 * -8 + z * -8) = 2(z + -3) + 3 13z + (-8 + -8z) = 2(z + -3) + 3 Reorder the terms: -8 + 13z + -8z = 2(z + -3) + 3 Combine like terms: 13z + -8z = 5z -8 + 5z = 2(z + -3) + 3 Reorder the terms: -8 + 5z = 2(-3 + z) + 3 -8 + 5z = (-3 * 2 + z * 2) + 3 -8 + 5z = (-6 + 2z) + 3 Reorder the terms: -8 + 5z = -6 + 3 + 2z Combine like terms: -6 + 3 = -3 -8 + 5z = -3 + 2z Solving -8 + 5z = -3 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -8 + 5z + -2z = -3 + 2z + -2z Combine like terms: 5z + -2z = 3z -8 + 3z = -3 + 2z + -2z Combine like terms: 2z + -2z = 0 -8 + 3z = -3 + 0 -8 + 3z = -3 Add '8' to each side of the equation. -8 + 8 + 3z = -3 + 8 Combine like terms: -8 + 8 = 0 0 + 3z = -3 + 8 3z = -3 + 8 Combine like terms: -3 + 8 = 5 3z = 5 Divide each side by '3'. z = 1.666666667 Simplifying z = 1.666666667
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