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Simplifying 8(4t + 1) + -16 = t + -1(t + 7) Reorder the terms: 8(1 + 4t) + -16 = t + -1(t + 7) (1 * 8 + 4t * 8) + -16 = t + -1(t + 7) (8 + 32t) + -16 = t + -1(t + 7) Reorder the terms: 8 + -16 + 32t = t + -1(t + 7) Combine like terms: 8 + -16 = -8 -8 + 32t = t + -1(t + 7) Reorder the terms: -8 + 32t = t + -1(7 + t) -8 + 32t = t + (7 * -1 + t * -1) -8 + 32t = t + (-7 + -1t) Reorder the terms: -8 + 32t = -7 + t + -1t Combine like terms: t + -1t = 0 -8 + 32t = -7 + 0 -8 + 32t = -7 Solving -8 + 32t = -7 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 32t = -7 + 8 Combine like terms: -8 + 8 = 0 0 + 32t = -7 + 8 32t = -7 + 8 Combine like terms: -7 + 8 = 1 32t = 1 Divide each side by '32'. t = 0.03125 Simplifying t = 0.03125
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