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Simplifying 5(t + -2) + 6(t + 1) + -1(t + 2) + 3 = 17 Reorder the terms: 5(-2 + t) + 6(t + 1) + -1(t + 2) + 3 = 17 (-2 * 5 + t * 5) + 6(t + 1) + -1(t + 2) + 3 = 17 (-10 + 5t) + 6(t + 1) + -1(t + 2) + 3 = 17 Reorder the terms: -10 + 5t + 6(1 + t) + -1(t + 2) + 3 = 17 -10 + 5t + (1 * 6 + t * 6) + -1(t + 2) + 3 = 17 -10 + 5t + (6 + 6t) + -1(t + 2) + 3 = 17 Reorder the terms: -10 + 5t + 6 + 6t + -1(2 + t) + 3 = 17 -10 + 5t + 6 + 6t + (2 * -1 + t * -1) + 3 = 17 -10 + 5t + 6 + 6t + (-2 + -1t) + 3 = 17 Reorder the terms: -10 + 6 + -2 + 3 + 5t + 6t + -1t = 17 Combine like terms: -10 + 6 = -4 -4 + -2 + 3 + 5t + 6t + -1t = 17 Combine like terms: -4 + -2 = -6 -6 + 3 + 5t + 6t + -1t = 17 Combine like terms: -6 + 3 = -3 -3 + 5t + 6t + -1t = 17 Combine like terms: 5t + 6t = 11t -3 + 11t + -1t = 17 Combine like terms: 11t + -1t = 10t -3 + 10t = 17 Solving -3 + 10t = 17 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 10t = 17 + 3 Combine like terms: -3 + 3 = 0 0 + 10t = 17 + 3 10t = 17 + 3 Combine like terms: 17 + 3 = 20 10t = 20 Divide each side by '10'. t = 2 Simplifying t = 2
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