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Simplifying 4(t + -2) + -7(4t + -1) = 14 + -8(5t + 4) Reorder the terms: 4(-2 + t) + -7(4t + -1) = 14 + -8(5t + 4) (-2 * 4 + t * 4) + -7(4t + -1) = 14 + -8(5t + 4) (-8 + 4t) + -7(4t + -1) = 14 + -8(5t + 4) Reorder the terms: -8 + 4t + -7(-1 + 4t) = 14 + -8(5t + 4) -8 + 4t + (-1 * -7 + 4t * -7) = 14 + -8(5t + 4) -8 + 4t + (7 + -28t) = 14 + -8(5t + 4) Reorder the terms: -8 + 7 + 4t + -28t = 14 + -8(5t + 4) Combine like terms: -8 + 7 = -1 -1 + 4t + -28t = 14 + -8(5t + 4) Combine like terms: 4t + -28t = -24t -1 + -24t = 14 + -8(5t + 4) Reorder the terms: -1 + -24t = 14 + -8(4 + 5t) -1 + -24t = 14 + (4 * -8 + 5t * -8) -1 + -24t = 14 + (-32 + -40t) Combine like terms: 14 + -32 = -18 -1 + -24t = -18 + -40t Solving -1 + -24t = -18 + -40t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40t' to each side of the equation. -1 + -24t + 40t = -18 + -40t + 40t Combine like terms: -24t + 40t = 16t -1 + 16t = -18 + -40t + 40t Combine like terms: -40t + 40t = 0 -1 + 16t = -18 + 0 -1 + 16t = -18 Add '1' to each side of the equation. -1 + 1 + 16t = -18 + 1 Combine like terms: -1 + 1 = 0 0 + 16t = -18 + 1 16t = -18 + 1 Combine like terms: -18 + 1 = -17 16t = -17 Divide each side by '16'. t = -1.0625 Simplifying t = -1.0625
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