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Simplifying 4(120 + -1z) + 10(120 + -1z) = 1176 (120 * 4 + -1z * 4) + 10(120 + -1z) = 1176 (480 + -4z) + 10(120 + -1z) = 1176 480 + -4z + (120 * 10 + -1z * 10) = 1176 480 + -4z + (1200 + -10z) = 1176 Reorder the terms: 480 + 1200 + -4z + -10z = 1176 Combine like terms: 480 + 1200 = 1680 1680 + -4z + -10z = 1176 Combine like terms: -4z + -10z = -14z 1680 + -14z = 1176 Solving 1680 + -14z = 1176 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1680' to each side of the equation. 1680 + -1680 + -14z = 1176 + -1680 Combine like terms: 1680 + -1680 = 0 0 + -14z = 1176 + -1680 -14z = 1176 + -1680 Combine like terms: 1176 + -1680 = -504 -14z = -504 Divide each side by '-14'. z = 36 Simplifying z = 36
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