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Simplifying 12(z + -4) + -10(z + 3) = 24 Reorder the terms: 12(-4 + z) + -10(z + 3) = 24 (-4 * 12 + z * 12) + -10(z + 3) = 24 (-48 + 12z) + -10(z + 3) = 24 Reorder the terms: -48 + 12z + -10(3 + z) = 24 -48 + 12z + (3 * -10 + z * -10) = 24 -48 + 12z + (-30 + -10z) = 24 Reorder the terms: -48 + -30 + 12z + -10z = 24 Combine like terms: -48 + -30 = -78 -78 + 12z + -10z = 24 Combine like terms: 12z + -10z = 2z -78 + 2z = 24 Solving -78 + 2z = 24 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '78' to each side of the equation. -78 + 78 + 2z = 24 + 78 Combine like terms: -78 + 78 = 0 0 + 2z = 24 + 78 2z = 24 + 78 Combine like terms: 24 + 78 = 102 2z = 102 Divide each side by '2'. z = 51 Simplifying z = 51
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