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Simplifying -9(t + 4) + 8(3t + 1) = (t + -4) + 7 Reorder the terms: -9(4 + t) + 8(3t + 1) = (t + -4) + 7 (4 * -9 + t * -9) + 8(3t + 1) = (t + -4) + 7 (-36 + -9t) + 8(3t + 1) = (t + -4) + 7 Reorder the terms: -36 + -9t + 8(1 + 3t) = (t + -4) + 7 -36 + -9t + (1 * 8 + 3t * 8) = (t + -4) + 7 -36 + -9t + (8 + 24t) = (t + -4) + 7 Reorder the terms: -36 + 8 + -9t + 24t = (t + -4) + 7 Combine like terms: -36 + 8 = -28 -28 + -9t + 24t = (t + -4) + 7 Combine like terms: -9t + 24t = 15t -28 + 15t = (t + -4) + 7 Reorder the terms: -28 + 15t = (-4 + t) + 7 Remove parenthesis around (-4 + t) -28 + 15t = -4 + t + 7 Reorder the terms: -28 + 15t = -4 + 7 + t Combine like terms: -4 + 7 = 3 -28 + 15t = 3 + t Solving -28 + 15t = 3 + t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1t' to each side of the equation. -28 + 15t + -1t = 3 + t + -1t Combine like terms: 15t + -1t = 14t -28 + 14t = 3 + t + -1t Combine like terms: t + -1t = 0 -28 + 14t = 3 + 0 -28 + 14t = 3 Add '28' to each side of the equation. -28 + 28 + 14t = 3 + 28 Combine like terms: -28 + 28 = 0 0 + 14t = 3 + 28 14t = 3 + 28 Combine like terms: 3 + 28 = 31 14t = 31 Divide each side by '14'. t = 2.214285714 Simplifying t = 2.214285714
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