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Simplifying 3(t + -7) + -5(2t + -7) = 22 + -8(3t + 5) Reorder the terms: 3(-7 + t) + -5(2t + -7) = 22 + -8(3t + 5) (-7 * 3 + t * 3) + -5(2t + -7) = 22 + -8(3t + 5) (-21 + 3t) + -5(2t + -7) = 22 + -8(3t + 5) Reorder the terms: -21 + 3t + -5(-7 + 2t) = 22 + -8(3t + 5) -21 + 3t + (-7 * -5 + 2t * -5) = 22 + -8(3t + 5) -21 + 3t + (35 + -10t) = 22 + -8(3t + 5) Reorder the terms: -21 + 35 + 3t + -10t = 22 + -8(3t + 5) Combine like terms: -21 + 35 = 14 14 + 3t + -10t = 22 + -8(3t + 5) Combine like terms: 3t + -10t = -7t 14 + -7t = 22 + -8(3t + 5) Reorder the terms: 14 + -7t = 22 + -8(5 + 3t) 14 + -7t = 22 + (5 * -8 + 3t * -8) 14 + -7t = 22 + (-40 + -24t) Combine like terms: 22 + -40 = -18 14 + -7t = -18 + -24t Solving 14 + -7t = -18 + -24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24t' to each side of the equation. 14 + -7t + 24t = -18 + -24t + 24t Combine like terms: -7t + 24t = 17t 14 + 17t = -18 + -24t + 24t Combine like terms: -24t + 24t = 0 14 + 17t = -18 + 0 14 + 17t = -18 Add '-14' to each side of the equation. 14 + -14 + 17t = -18 + -14 Combine like terms: 14 + -14 = 0 0 + 17t = -18 + -14 17t = -18 + -14 Combine like terms: -18 + -14 = -32 17t = -32 Divide each side by '17'. t = -1.882352941 Simplifying t = -1.882352941
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