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Simplifying (t + 42) * 3 = (t + 126) * 7 Reorder the terms: (42 + t) * 3 = (t + 126) * 7 Reorder the terms for easier multiplication: 3(42 + t) = (t + 126) * 7 (42 * 3 + t * 3) = (t + 126) * 7 (126 + 3t) = (t + 126) * 7 Reorder the terms: 126 + 3t = (126 + t) * 7 Reorder the terms for easier multiplication: 126 + 3t = 7(126 + t) 126 + 3t = (126 * 7 + t * 7) 126 + 3t = (882 + 7t) Solving 126 + 3t = 882 + 7t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7t' to each side of the equation. 126 + 3t + -7t = 882 + 7t + -7t Combine like terms: 3t + -7t = -4t 126 + -4t = 882 + 7t + -7t Combine like terms: 7t + -7t = 0 126 + -4t = 882 + 0 126 + -4t = 882 Add '-126' to each side of the equation. 126 + -126 + -4t = 882 + -126 Combine like terms: 126 + -126 = 0 0 + -4t = 882 + -126 -4t = 882 + -126 Combine like terms: 882 + -126 = 756 -4t = 756 Divide each side by '-4'. t = -189 Simplifying t = -189
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