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Simplifying 7(t + -3) + 32t = 9(t + 1) Reorder the terms: 7(-3 + t) + 32t = 9(t + 1) (-3 * 7 + t * 7) + 32t = 9(t + 1) (-21 + 7t) + 32t = 9(t + 1) Combine like terms: 7t + 32t = 39t -21 + 39t = 9(t + 1) Reorder the terms: -21 + 39t = 9(1 + t) -21 + 39t = (1 * 9 + t * 9) -21 + 39t = (9 + 9t) Solving -21 + 39t = 9 + 9t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9t' to each side of the equation. -21 + 39t + -9t = 9 + 9t + -9t Combine like terms: 39t + -9t = 30t -21 + 30t = 9 + 9t + -9t Combine like terms: 9t + -9t = 0 -21 + 30t = 9 + 0 -21 + 30t = 9 Add '21' to each side of the equation. -21 + 21 + 30t = 9 + 21 Combine like terms: -21 + 21 = 0 0 + 30t = 9 + 21 30t = 9 + 21 Combine like terms: 9 + 21 = 30 30t = 30 Divide each side by '30'. t = 1 Simplifying t = 1
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