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Simplifying 4[z + -1(3z + 29) + 9] = 3(z + 10) Reorder the terms: 4[z + -1(29 + 3z) + 9] = 3(z + 10) 4[z + (29 * -1 + 3z * -1) + 9] = 3(z + 10) 4[z + (-29 + -3z) + 9] = 3(z + 10) Reorder the terms: 4[-29 + 9 + z + -3z] = 3(z + 10) Combine like terms: -29 + 9 = -20 4[-20 + z + -3z] = 3(z + 10) Combine like terms: z + -3z = -2z 4[-20 + -2z] = 3(z + 10) [-20 * 4 + -2z * 4] = 3(z + 10) [-80 + -8z] = 3(z + 10) Reorder the terms: -80 + -8z = 3(10 + z) -80 + -8z = (10 * 3 + z * 3) -80 + -8z = (30 + 3z) Solving -80 + -8z = 30 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -80 + -8z + -3z = 30 + 3z + -3z Combine like terms: -8z + -3z = -11z -80 + -11z = 30 + 3z + -3z Combine like terms: 3z + -3z = 0 -80 + -11z = 30 + 0 -80 + -11z = 30 Add '80' to each side of the equation. -80 + 80 + -11z = 30 + 80 Combine like terms: -80 + 80 = 0 0 + -11z = 30 + 80 -11z = 30 + 80 Combine like terms: 30 + 80 = 110 -11z = 110 Divide each side by '-11'. z = -10 Simplifying z = -10
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