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Simplifying 8(z + -6) + -1(-5z + -1) = 12z Reorder the terms: 8(-6 + z) + -1(-5z + -1) = 12z (-6 * 8 + z * 8) + -1(-5z + -1) = 12z (-48 + 8z) + -1(-5z + -1) = 12z Reorder the terms: -48 + 8z + -1(-1 + -5z) = 12z -48 + 8z + (-1 * -1 + -5z * -1) = 12z -48 + 8z + (1 + 5z) = 12z Reorder the terms: -48 + 1 + 8z + 5z = 12z Combine like terms: -48 + 1 = -47 -47 + 8z + 5z = 12z Combine like terms: 8z + 5z = 13z -47 + 13z = 12z Solving -47 + 13z = 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. -47 + 13z + -12z = 12z + -12z Combine like terms: 13z + -12z = 1z -47 + 1z = 12z + -12z Combine like terms: 12z + -12z = 0 -47 + 1z = 0 Add '47' to each side of the equation. -47 + 47 + 1z = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 1z = 0 + 47 1z = 0 + 47 Combine like terms: 0 + 47 = 47 1z = 47 Divide each side by '1'. z = 47 Simplifying z = 47
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