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Simplifying 10[z + -1(9z + 18) + 10] = 5(z + 1) Reorder the terms: 10[z + -1(18 + 9z) + 10] = 5(z + 1) 10[z + (18 * -1 + 9z * -1) + 10] = 5(z + 1) 10[z + (-18 + -9z) + 10] = 5(z + 1) Reorder the terms: 10[-18 + 10 + z + -9z] = 5(z + 1) Combine like terms: -18 + 10 = -8 10[-8 + z + -9z] = 5(z + 1) Combine like terms: z + -9z = -8z 10[-8 + -8z] = 5(z + 1) [-8 * 10 + -8z * 10] = 5(z + 1) [-80 + -80z] = 5(z + 1) Reorder the terms: -80 + -80z = 5(1 + z) -80 + -80z = (1 * 5 + z * 5) -80 + -80z = (5 + 5z) Solving -80 + -80z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -80 + -80z + -5z = 5 + 5z + -5z Combine like terms: -80z + -5z = -85z -80 + -85z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -80 + -85z = 5 + 0 -80 + -85z = 5 Add '80' to each side of the equation. -80 + 80 + -85z = 5 + 80 Combine like terms: -80 + 80 = 0 0 + -85z = 5 + 80 -85z = 5 + 80 Combine like terms: 5 + 80 = 85 -85z = 85 Divide each side by '-85'. z = -1 Simplifying z = -1
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