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Simplifying 1[-4z + 6 + 7(z + 1)] = -5z + 4 Reorder the terms: 1[-4z + 6 + 7(1 + z)] = -5z + 4 1[-4z + 6 + (1 * 7 + z * 7)] = -5z + 4 1[-4z + 6 + (7 + 7z)] = -5z + 4 Reorder the terms: 1[6 + 7 + -4z + 7z] = -5z + 4 Combine like terms: 6 + 7 = 13 1[13 + -4z + 7z] = -5z + 4 Combine like terms: -4z + 7z = 3z 1[13 + 3z] = -5z + 4 [13 * 1 + 3z * 1] = -5z + 4 [13 + 3z] = -5z + 4 Reorder the terms: 13 + 3z = 4 + -5z Solving 13 + 3z = 4 + -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. 13 + 3z + 5z = 4 + -5z + 5z Combine like terms: 3z + 5z = 8z 13 + 8z = 4 + -5z + 5z Combine like terms: -5z + 5z = 0 13 + 8z = 4 + 0 13 + 8z = 4 Add '-13' to each side of the equation. 13 + -13 + 8z = 4 + -13 Combine like terms: 13 + -13 = 0 0 + 8z = 4 + -13 8z = 4 + -13 Combine like terms: 4 + -13 = -9 8z = -9 Divide each side by '8'. z = -1.125 Simplifying z = -1.125
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