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Simplifying 2(t + -2) + -3(2t + -7) = 10 + -8(4t + 3) Reorder the terms: 2(-2 + t) + -3(2t + -7) = 10 + -8(4t + 3) (-2 * 2 + t * 2) + -3(2t + -7) = 10 + -8(4t + 3) (-4 + 2t) + -3(2t + -7) = 10 + -8(4t + 3) Reorder the terms: -4 + 2t + -3(-7 + 2t) = 10 + -8(4t + 3) -4 + 2t + (-7 * -3 + 2t * -3) = 10 + -8(4t + 3) -4 + 2t + (21 + -6t) = 10 + -8(4t + 3) Reorder the terms: -4 + 21 + 2t + -6t = 10 + -8(4t + 3) Combine like terms: -4 + 21 = 17 17 + 2t + -6t = 10 + -8(4t + 3) Combine like terms: 2t + -6t = -4t 17 + -4t = 10 + -8(4t + 3) Reorder the terms: 17 + -4t = 10 + -8(3 + 4t) 17 + -4t = 10 + (3 * -8 + 4t * -8) 17 + -4t = 10 + (-24 + -32t) Combine like terms: 10 + -24 = -14 17 + -4t = -14 + -32t Solving 17 + -4t = -14 + -32t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '32t' to each side of the equation. 17 + -4t + 32t = -14 + -32t + 32t Combine like terms: -4t + 32t = 28t 17 + 28t = -14 + -32t + 32t Combine like terms: -32t + 32t = 0 17 + 28t = -14 + 0 17 + 28t = -14 Add '-17' to each side of the equation. 17 + -17 + 28t = -14 + -17 Combine like terms: 17 + -17 = 0 0 + 28t = -14 + -17 28t = -14 + -17 Combine like terms: -14 + -17 = -31 28t = -31 Divide each side by '28'. t = -1.107142857 Simplifying t = -1.107142857
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