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Simplifying (7t + -2) * 9 + -1(3t + 1) = -3(1 + -3t) Reorder the terms: (-2 + 7t) * 9 + -1(3t + 1) = -3(1 + -3t) Reorder the terms for easier multiplication: 9(-2 + 7t) + -1(3t + 1) = -3(1 + -3t) (-2 * 9 + 7t * 9) + -1(3t + 1) = -3(1 + -3t) (-18 + 63t) + -1(3t + 1) = -3(1 + -3t) Reorder the terms: -18 + 63t + -1(1 + 3t) = -3(1 + -3t) -18 + 63t + (1 * -1 + 3t * -1) = -3(1 + -3t) -18 + 63t + (-1 + -3t) = -3(1 + -3t) Reorder the terms: -18 + -1 + 63t + -3t = -3(1 + -3t) Combine like terms: -18 + -1 = -19 -19 + 63t + -3t = -3(1 + -3t) Combine like terms: 63t + -3t = 60t -19 + 60t = -3(1 + -3t) -19 + 60t = (1 * -3 + -3t * -3) -19 + 60t = (-3 + 9t) Solving -19 + 60t = -3 + 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. -19 + 60t + -9t = -3 + 9t + -9t Combine like terms: 60t + -9t = 51t -19 + 51t = -3 + 9t + -9t Combine like terms: 9t + -9t = 0 -19 + 51t = -3 + 0 -19 + 51t = -3 Add '19' to each side of the equation. -19 + 19 + 51t = -3 + 19 Combine like terms: -19 + 19 = 0 0 + 51t = -3 + 19 51t = -3 + 19 Combine like terms: -3 + 19 = 16 51t = 16 Divide each side by '51'. t = 0.3137254902 Simplifying t = 0.3137254902
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