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Simplifying 3[z + -1(5z + 45) + 5] = 5(z + 10) Reorder the terms: 3[z + -1(45 + 5z) + 5] = 5(z + 10) 3[z + (45 * -1 + 5z * -1) + 5] = 5(z + 10) 3[z + (-45 + -5z) + 5] = 5(z + 10) Reorder the terms: 3[-45 + 5 + z + -5z] = 5(z + 10) Combine like terms: -45 + 5 = -40 3[-40 + z + -5z] = 5(z + 10) Combine like terms: z + -5z = -4z 3[-40 + -4z] = 5(z + 10) [-40 * 3 + -4z * 3] = 5(z + 10) [-120 + -12z] = 5(z + 10) Reorder the terms: -120 + -12z = 5(10 + z) -120 + -12z = (10 * 5 + z * 5) -120 + -12z = (50 + 5z) Solving -120 + -12z = 50 + 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. -120 + -12z + -5z = 50 + 5z + -5z Combine like terms: -12z + -5z = -17z -120 + -17z = 50 + 5z + -5z Combine like terms: 5z + -5z = 0 -120 + -17z = 50 + 0 -120 + -17z = 50 Add '120' to each side of the equation. -120 + 120 + -17z = 50 + 120 Combine like terms: -120 + 120 = 0 0 + -17z = 50 + 120 -17z = 50 + 120 Combine like terms: 50 + 120 = 170 -17z = 170 Divide each side by '-17'. z = -10 Simplifying z = -10
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