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Simplifying 8 + 4(-5z + 6) = -6(2z + -8) + -7 Reorder the terms: 8 + 4(6 + -5z) = -6(2z + -8) + -7 8 + (6 * 4 + -5z * 4) = -6(2z + -8) + -7 8 + (24 + -20z) = -6(2z + -8) + -7 Combine like terms: 8 + 24 = 32 32 + -20z = -6(2z + -8) + -7 Reorder the terms: 32 + -20z = -6(-8 + 2z) + -7 32 + -20z = (-8 * -6 + 2z * -6) + -7 32 + -20z = (48 + -12z) + -7 Reorder the terms: 32 + -20z = 48 + -7 + -12z Combine like terms: 48 + -7 = 41 32 + -20z = 41 + -12z Solving 32 + -20z = 41 + -12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12z' to each side of the equation. 32 + -20z + 12z = 41 + -12z + 12z Combine like terms: -20z + 12z = -8z 32 + -8z = 41 + -12z + 12z Combine like terms: -12z + 12z = 0 32 + -8z = 41 + 0 32 + -8z = 41 Add '-32' to each side of the equation. 32 + -32 + -8z = 41 + -32 Combine like terms: 32 + -32 = 0 0 + -8z = 41 + -32 -8z = 41 + -32 Combine like terms: 41 + -32 = 9 -8z = 9 Divide each side by '-8'. z = -1.125 Simplifying z = -1.125
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