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Simplifying 3(t + -8) + -7(1 + -2t) = 16(t + -4) + 7 Reorder the terms: 3(-8 + t) + -7(1 + -2t) = 16(t + -4) + 7 (-8 * 3 + t * 3) + -7(1 + -2t) = 16(t + -4) + 7 (-24 + 3t) + -7(1 + -2t) = 16(t + -4) + 7 -24 + 3t + (1 * -7 + -2t * -7) = 16(t + -4) + 7 -24 + 3t + (-7 + 14t) = 16(t + -4) + 7 Reorder the terms: -24 + -7 + 3t + 14t = 16(t + -4) + 7 Combine like terms: -24 + -7 = -31 -31 + 3t + 14t = 16(t + -4) + 7 Combine like terms: 3t + 14t = 17t -31 + 17t = 16(t + -4) + 7 Reorder the terms: -31 + 17t = 16(-4 + t) + 7 -31 + 17t = (-4 * 16 + t * 16) + 7 -31 + 17t = (-64 + 16t) + 7 Reorder the terms: -31 + 17t = -64 + 7 + 16t Combine like terms: -64 + 7 = -57 -31 + 17t = -57 + 16t Solving -31 + 17t = -57 + 16t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16t' to each side of the equation. -31 + 17t + -16t = -57 + 16t + -16t Combine like terms: 17t + -16t = 1t -31 + 1t = -57 + 16t + -16t Combine like terms: 16t + -16t = 0 -31 + 1t = -57 + 0 -31 + 1t = -57 Add '31' to each side of the equation. -31 + 31 + 1t = -57 + 31 Combine like terms: -31 + 31 = 0 0 + 1t = -57 + 31 1t = -57 + 31 Combine like terms: -57 + 31 = -26 1t = -26 Divide each side by '1'. t = -26 Simplifying t = -26
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