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Simplifying 8(5t + 1) = 16(t + 5) + 16(t + -3) Reorder the terms: 8(1 + 5t) = 16(t + 5) + 16(t + -3) (1 * 8 + 5t * 8) = 16(t + 5) + 16(t + -3) (8 + 40t) = 16(t + 5) + 16(t + -3) Reorder the terms: 8 + 40t = 16(5 + t) + 16(t + -3) 8 + 40t = (5 * 16 + t * 16) + 16(t + -3) 8 + 40t = (80 + 16t) + 16(t + -3) Reorder the terms: 8 + 40t = 80 + 16t + 16(-3 + t) 8 + 40t = 80 + 16t + (-3 * 16 + t * 16) 8 + 40t = 80 + 16t + (-48 + 16t) Reorder the terms: 8 + 40t = 80 + -48 + 16t + 16t Combine like terms: 80 + -48 = 32 8 + 40t = 32 + 16t + 16t Combine like terms: 16t + 16t = 32t 8 + 40t = 32 + 32t Solving 8 + 40t = 32 + 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. 8 + 40t + -32t = 32 + 32t + -32t Combine like terms: 40t + -32t = 8t 8 + 8t = 32 + 32t + -32t Combine like terms: 32t + -32t = 0 8 + 8t = 32 + 0 8 + 8t = 32 Add '-8' to each side of the equation. 8 + -8 + 8t = 32 + -8 Combine like terms: 8 + -8 = 0 0 + 8t = 32 + -8 8t = 32 + -8 Combine like terms: 32 + -8 = 24 8t = 24 Divide each side by '8'. t = 3 Simplifying t = 3
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