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Simplifying 3[4(0.25 + 0.5z) + -0.75z] = 3[8(0.50 + 0.25z)] 3[(0.25 * 4 + 0.5z * 4) + -0.75z] = 3[8(0.50 + 0.25z)] 3[(1 + 2z) + -0.75z] = 3[8(0.50 + 0.25z)] Combine like terms: 2z + -0.75z = 1.25z 3[1 + 1.25z] = 3[8(0.50 + 0.25z)] [1 * 3 + 1.25z * 3] = 3[8(0.50 + 0.25z)] [3 + 3.75z] = 3[8(0.50 + 0.25z)] 3 + 3.75z = 3[(0.50 * 8 + 0.25z * 8)] 3 + 3.75z = 3[(4 + 2z)] 3 + 3.75z = [4 * 3 + 2z * 3] 3 + 3.75z = [12 + 6z] Solving 3 + 3.75z = 12 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 3 + 3.75z + -6z = 12 + 6z + -6z Combine like terms: 3.75z + -6z = -2.25z 3 + -2.25z = 12 + 6z + -6z Combine like terms: 6z + -6z = 0 3 + -2.25z = 12 + 0 3 + -2.25z = 12 Add '-3' to each side of the equation. 3 + -3 + -2.25z = 12 + -3 Combine like terms: 3 + -3 = 0 0 + -2.25z = 12 + -3 -2.25z = 12 + -3 Combine like terms: 12 + -3 = 9 -2.25z = 9 Divide each side by '-2.25'. z = -4 Simplifying z = -4
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