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Simplifying 2[z + -1(10z + 69) + 6] = 3(z + 7) Reorder the terms: 2[z + -1(69 + 10z) + 6] = 3(z + 7) 2[z + (69 * -1 + 10z * -1) + 6] = 3(z + 7) 2[z + (-69 + -10z) + 6] = 3(z + 7) Reorder the terms: 2[-69 + 6 + z + -10z] = 3(z + 7) Combine like terms: -69 + 6 = -63 2[-63 + z + -10z] = 3(z + 7) Combine like terms: z + -10z = -9z 2[-63 + -9z] = 3(z + 7) [-63 * 2 + -9z * 2] = 3(z + 7) [-126 + -18z] = 3(z + 7) Reorder the terms: -126 + -18z = 3(7 + z) -126 + -18z = (7 * 3 + z * 3) -126 + -18z = (21 + 3z) Solving -126 + -18z = 21 + 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. -126 + -18z + -3z = 21 + 3z + -3z Combine like terms: -18z + -3z = -21z -126 + -21z = 21 + 3z + -3z Combine like terms: 3z + -3z = 0 -126 + -21z = 21 + 0 -126 + -21z = 21 Add '126' to each side of the equation. -126 + 126 + -21z = 21 + 126 Combine like terms: -126 + 126 = 0 0 + -21z = 21 + 126 -21z = 21 + 126 Combine like terms: 21 + 126 = 147 -21z = 147 Divide each side by '-21'. z = -7 Simplifying z = -7
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